Density Functional Theory Model for Adsorption-Induced Deformation of Mesoporous Materials with Nonconvex Pore Geometry

Abstract

Adsorption of fluids in nanoporous media causes mechanical stresses which result in deformation. This phenomenon is ubiquitous, and its magnitude depends on the pore size and geometry. Adsorption and adsorption-induced deformation are typically modeled in slit-shape or convex (cylindrical or spherical) pores. However, many porous materials are composed of spherical grains, so that the pores are formed by the intergranular spaces between the convex solid surfaces. Here, we present a first theoretical study of adsorption-induced deformation in nonconvex pores; in particular, we studied the templated mesoporous carbons. The model is based on classical density functional theory within the local density approximation applied to the description of hard-sphere interactions. We predict the adsorption isotherms and solvation pressure isotherms for nitrogen adsorption in CMK-3 carbons. The shape of the adsorption isotherm matches the shape of the experimental isotherm. The predicted solvation pressure isotherms are qualitatively different from the solvation pressure isotherms in cylindrical pores. We attribute this difference to the formation of liquid bridges between the adjacent rods. Our results suggest that adsorption-induced deformation in materials with nonconvex pores cannot be predicted within the existing models. These results may shed some light on understanding the adsorption-induced deformation of consolidated granular media.

Adsorption-induced deformation of hierarchical organised carbon materials with ordered, non-convex mesoporosity

“…Kolesnikov et al [52] have recently demonstrated that a bridged phase leads to significant compressive strain, as observed also experimentally in the present work. However, the deformation amplitude of the sample CN shows the larger (SANS) or similar (dilatometry) strain at p/p 0 ≈ 0.95 as compared to the two activated samples.…”

“…For the designated 'bridged phase' the strain recorded in SANS for all three samples increases slightly with relative pressure, but stays in the compressive regime in SANS until relative pressures associated with the filled phase are reached. The slight increase in strain contradicts the recent theoretical results from Kolesnikov et al [52], where the bridged phase leads to increasingly compressive strains only. Although the measured strain is generally compressive in the bridged regime, the clear deviation from the predicted behaviour of SANS strain isotherm demonstrates the necessity to consider other contributions, such as expansive strains originating from microporosity.…”

“…In this region, exclusively compressive strains are observed in SANS (Figure 5(a)). In recent theoretical considerations of adsorption-induced deformation in non-convex pores by Kolesnikov et al [52] no significant contraction was observed as a result of the separated phase. Additionally, analytical calculations (see section S2 in the SI, as well as Figure S3 and S4) which determine the stress and strain induced by the separated phase show that these should be exclusively expansive in nature.…”

“…The shape of the strain isotherms implies that some intermittent phase exists prior to the filling of the entire void space [43,52], as three relative pressure intervals with distinct behaviour can be distinguished. Recent theoretical work on the solvation pressure inside the void space in between 2D-hexagonally arranged carbon nanorods [43,52] confirms that the shape of strain isotherms observed with SANS could be due to some sort of 'bridged-phase', although the relative pressure interval where it should be stable might overlap significantly with the 'filled phase' due to the disordered nature of the mesopore space.…”

“…We will address the effective elastic moduli determined from SANS and dilatometry with Equation 5by M SANS and M Dil , respectively. On the mesopore scale, we assume that interconnections between adjacent carbon nanorods are most likely to deform predominately in conjunction with recent considerations [52]. But since the density and geometric arrangement of these interconnections is completely unknown, we initially refrain from assuming any detailed mechanism and consider the values of M SANS and M Dil as representative values of the system stiffness under the given mechanical 'pore load'.…”