Abstract
Commonly, the confinement effects are studied from the grand canonical Monte Carlo (GCMC) simulations from the computation of the density of liquid in the confined phase. The GCMC modeling and chemical potential (μ) calculations are based on the insertion/deletion of the real and ghost particle, respectively. At high density, i.e., at high pressure or low temperature, the insertions fail from the Widom insertions while the performing methods as expanded method or perturbation approach are not efficient to treat the large and complex molecules. To overcome this problem we use a simple and efficient method to compute the liquid's density in the confined medium. This method does not require the precalculation of μ and is an alternative to the GCMC simulations. From the isothermal–isosurface–isobaric statistical ensemble we consider the explicit framework/liquid external interface to model an explicit liquid's reservoir. In this procedure only the liquid molecules undergo the volume changes while the volume of the framework is kept constant. Therefore, this method is described in the Np _{ n } AV _{ f } Tstatistical ensemble, where N is the number of particles, p _{ n } is the normal pressure, V _{ f } is the volume of framework, A is the surface of the solid/fluid interface, and T is the temperature. This approach is applied and validated from the computation of the density of the methanol and water confined in the mesoporous cylindrical silicananopores and the MIL-53(Cr) metal organic framework type, respectively.
I. INTRODUCTION
II. ISOTHERMAL–ISOSURFACE–ISOBARIC (III) STATISTICAL ENSEMBLE:Np _{ n } AV _{ f } T
III. EXPLICIT SOLID/LIQUID INTERFACE
IV. FORCE FIELD AND COMPUTATIONAL PROCEDURE
V. RESULTS AND DISCUSSION
VI. SUMMARY
Key Topics
- Liquid solid interfaces
- 23.0
- Liquid surfaces
- 15.0
- Nanoporous materials
- 11.0
- Chemical potential
- 10.0
- Classical ensemble theory
- 8.0
Figures
(a) Snapshot of the external and internal interfaces in the silica nanopore represented from a Connolly surface. The oxygen, hydrogen, and silicon atoms are represented in red, white, and yellow, respectively. (b) Scheme of principle of our method in the isothermal–isosurface–isobaric statistical ensemble.
(a) Snapshot of the external and internal interfaces in the silica nanopore represented from a Connolly surface. The oxygen, hydrogen, and silicon atoms are represented in red, white, and yellow, respectively. (b) Scheme of principle of our method in the isothermal–isosurface–isobaric statistical ensemble.
Snapshots of the silica nanopore and MIL-53(Cr) according to two planes (xy and xz) and z axis. (Carbon atoms are represented in blue and gray color, oxygen atoms in red, hydrogen in white, and silicon in yellow.)
Snapshots of the silica nanopore and MIL-53(Cr) according to two planes (xy and xz) and z axis. (Carbon atoms are represented in blue and gray color, oxygen atoms in red, hydrogen in white, and silicon in yellow.)
(a) Density of methanol in the bulk and confined phases for HH framework. (•) and (■) represent the experimental densities (Ref. 60) of the bulk and confined phases. (○) and (□) are the computed bulk and confined densities obtained from III. (×) is the confined density obtained from the GCMC simulation () [(*) = excess)] and (⋆) is the density of bulk phase obtained from NpT simulations. (■) are the results obtained from with R = 10 Å (vertical line in panel b). Average of error bars for III was 7 kg m^{−3} while for GCMC we calculate 4 kg m^{−3} as error. (b) Radial density of methanol in HH at T = 300K (solid line), in WH at T = 300 K (dashed line). Bulk phase density (•) and average density obtained from radial profile (■). (c) Radial density of methanol in HH from GCMC simulation (solid line) and our method (dotted line).
(a) Density of methanol in the bulk and confined phases for HH framework. (•) and (■) represent the experimental densities (Ref. 60) of the bulk and confined phases. (○) and (□) are the computed bulk and confined densities obtained from III. (×) is the confined density obtained from the GCMC simulation () [(*) = excess)] and (⋆) is the density of bulk phase obtained from NpT simulations. (■) are the results obtained from with R = 10 Å (vertical line in panel b). Average of error bars for III was 7 kg m^{−3} while for GCMC we calculate 4 kg m^{−3} as error. (b) Radial density of methanol in HH at T = 300K (solid line), in WH at T = 300 K (dashed line). Bulk phase density (•) and average density obtained from radial profile (■). (c) Radial density of methanol in HH from GCMC simulation (solid line) and our method (dotted line).
Profile of number of molecules along to z axis in HH (a) and in MIL-53(Cr) (b). In panel (b) we add in inset the profile of oxygen atoms to highlight the density's correlation.
Profile of number of molecules along to z axis in HH (a) and in MIL-53(Cr) (b). In panel (b) we add in inset the profile of oxygen atoms to highlight the density's correlation.
Normal pressure as a function of time for HH (solid line and bottom axis) and MIL-53(Cr) (dashed line and top axis).
Normal pressure as a function of time for HH (solid line and bottom axis) and MIL-53(Cr) (dashed line and top axis).
(a) Total component of the normal pressure parallel to the z axis for HH. (b) Profile of transverse (solid line and left axis) and normal (dashed line and right axis) component of host/guest pressure contribution. (c) p _{ n } − p _{ t } as a function of z. For (b) and (c) we provided an enlargement between z = 30 and z = 40.
(a) Total component of the normal pressure parallel to the z axis for HH. (b) Profile of transverse (solid line and left axis) and normal (dashed line and right axis) component of host/guest pressure contribution. (c) p _{ n } − p _{ t } as a function of z. For (b) and (c) we provided an enlargement between z = 30 and z = 40.
(a) Profile of MIL-53(Cr)/water contribution to the normal (solid line) and transverse pressure (dashed line). Enlargement is provided between z = −35 and z = −15. (b) and (c) Profile of the number of atoms belonging to the MIL-53(Cr) according to the z axis and p _{ n } − p _{ t }, respectively.
(a) Profile of MIL-53(Cr)/water contribution to the normal (solid line) and transverse pressure (dashed line). Enlargement is provided between z = −35 and z = −15. (b) and (c) Profile of the number of atoms belonging to the MIL-53(Cr) according to the z axis and p _{ n } − p _{ t }, respectively.
Tables
Structural characteristics of simulations. L _{α} are the lengths of the boxes along the three axes (α = x, y, z). is the length of framework according to z and N _{ l } is the number of liquid molecules. For the silica nanopore (WH/HH) and MIL-53(Cr) the inserted molecules are methanol and water, respectively.
Structural characteristics of simulations. L _{α} are the lengths of the boxes along the three axes (α = x, y, z). is the length of framework according to z and N _{ l } is the number of liquid molecules. For the silica nanopore (WH/HH) and MIL-53(Cr) the inserted molecules are methanol and water, respectively.
Density (ρ) and number (n) of water and methanol molecules in the bulk (B) and confined (C) phases for the highly and weakly hydrated silica nanopores and the MIL-53(Cr) MOF type. (III) indicates the isothermal–isosurface–isobaric statistical ensemble.
Density (ρ) and number (n) of water and methanol molecules in the bulk (B) and confined (C) phases for the highly and weakly hydrated silica nanopores and the MIL-53(Cr) MOF type. (III) indicates the isothermal–isosurface–isobaric statistical ensemble.
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