Unexpected sorption-induced deformation of nanoporous glass: evidence for spatial rearrangement of adsorbed argon

Stress or Strain Does Not Impact Sorption in Stiff Mesoporous Materials

The present paper investigates strain-induced sorption in mesoporous silicon. Contrarily to a previous report based on indirect evidence, we find that external mechanical strain or stress has no measurable impact on sorption isotherms, down to a relative accuracy of 10^-3. This conclusion is in agreement with the analysis of the sorption-induced strain of porous silicon and holds for other stiff mesoporous materials such as porous silicas.

Experimental Method for the Determination of the Saturation Vapor Pressure above Supercooled Nanoconfined Liquids

For sorption studies, the saturation vapor pressure p ₀ above an adsorbate is of great significance. For example, it is needed for the determination of the pore size distribution, the Laplace pressure, and the chemical potential. Above the bulk triple point, T ₃ ^bulk, this pressure is identical with the saturation vapor pressure above the bulk liquid. However, below T ₃ ^bulk, the correct value of p ₀(T) is controversial. Nanoconfined fluids exhibit a shift of the freezing and melting temperatures in comparison to the bulk state. Thus, the adsorbed fluid is supercooled in a certain temperature range below T ₃ ^bulk. Here, we show that it is possible to determine the appropriate saturation vapor pressure above the nanoconfined supercooled liquid experimentally. For this purpose, we have performed sorption measurements with liquid argon in nanoporous Vycor glass in the temperature range of the supercooled liquid and at temperatures above the bulk triple point. In order to determine the unknown and temperature-dependent saturation vapor pressure of the supercooled confined adsorbate, p ₀(T), we use the Kelvin equation relating this quantity to the pore radius, r _P(p ₀), that is independent of temperature. The knowledge of the absolute values for the liquid-vapor surface tension of the supercooled adsorbate, γ_lv(T), is not required. However, we presuppose that its dependence on the unknown vapor pressure, γ_lv(p ₀), is bulk-like. Our results indicate that the saturation vapor pressure above the supercooled nanoconfined liquid corresponds to that above supercooled bulk argon (i.e., to the pressure obtained by an extension of the usual vaporization curve to T < T ₃ ^bulk). We expect that this method can be used for the determination of p ₀ above other supercooled adsorbates.

Capillary Stress and Structural Relaxation in Moist Granular Materials

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

Mechanical Characterization of Hierarchical Structured Porous Silica by in Situ Dilatometry Measurements during Gas Adsorption

Mechanical properties of hierarchically structured nanoporous materials are determined by the solid phase stiffness and the pore network morphology. We analyze the mechanical stiffness of hierarchically structured silica monoliths synthesized via a sol-gel process, which possess a macroporous scaffold built of interconnected struts with hexagonally ordered cylindrical mesopores. We consider samples with and without microporosity within the mesopore walls and analyze them on the macroscopic level as well as on the microscopic level of the mesopores. Untreated as-prepared samples still containing some organic components and the respective calcined and sintered counterparts of varying microporosity are investigated. To determine Young's moduli on the level of the macroscopic monoliths, we apply ultrasonic run time measurements, while Young's moduli of the mesopore walls are obtained by analysis of the in situ strain isotherms during N₂ adsorption at 77 K. For the latter, we extended our previously reported theoretical approach for this type of materials by incorporating the micropore effects, which are clearly not negligible in the calcined and most of the sintered samples. The comparison of the macro- and microscopic Young's moduli reveals that both properties follow essentially the same trends, that is, calcination and sintering increase the mechanical stiffness on both levels. Consequently, stiffening of the monolithic samples can be primarily attributed to stiffening of the backbone material which is consistent with the fact that the morphology on the mesopore level is mainly preserved with the post-treatments applied.

Requirements to Determine the Average Pore Size of Nanoporous Media Using Ultrasound

Liquids in nanoporous media are exposed to an adsorption-induced pressure, a consequence of the interaction with the pore surface. The smaller the pore diameter, d P, the higher the pressure at saturation and thus the bulk modulus of the confined liquid. Therefore, it has been proposed to use ultrasonic measurements on saturated nanoporous media for the determination of the average pore size. Here, we discuss the requirements for such an analysis. Although predictions for the size-dependent pore pressure and the liquid's modulus, K iso(d P), are based on isothermal simulations, an experimentalist studying the propagation of ultrasonic waves determines adiabatic moduli, K ad(d P). We show that the quantity relating adiabatic and isothermal moduli, the heat capacity ratio γ = c p/c v = K ad/K iso, exhibits a strong pressure dependence for many bulk liquids. In nanopores, this translates into a size-dependent γ(d P), provided the confinement does not alter the heat capacity ratio. Disregarding this effect in the analysis of ultrasonic data would yield an underestimate of the isothermal modulus and thus an overestimate of the average pore size. For a correct analysis, an experimentalist thus needs to know the size dependence of three quantities: the isothermal modulus, adsorption-induced pressure, and heat capacity ratio.

Effect of pore geometry on the compressibility of a confined simple fluid

Fluids confined in nanopores exhibit properties different from the properties of the same fluids in bulk; among these properties is the isothermal compressibility or elastic modulus. The modulus of a fluid in nanopores can be extracted from ultrasonic experiments or calculated from molecular simulations. Using Monte Carlo simulations in the grand canonical ensemble, we calculated the modulus for liquid argon at its normal boiling point (87.3 K) adsorbed in model silica pores of two different morphologies and various sizes. For spherical pores, for all the pore sizes (diameters) exceeding 2 nm, we obtained a logarithmic dependence of fluid modulus on the vapor pressure. Calculation of the modulus at saturation showed that the modulus of the fluid in spherical pores is a linear function of the reciprocal pore size. The calculation of the modulus of the fluid in cylindrical pores appeared too scattered to make quantitative conclusions. We performed additional simulations at higher temperature (119.6 K), at which Monte Carlo insertions and removals become more efficient. The results of the simulations at higher temperature confirmed both regularities for cylindrical pores and showed quantitative difference between the fluid moduli in pores of different geometries. Both of the observed regularities for the modulus stem from the Tait-Murnaghan equation applied to the confined fluid. Our results, along with the development of the effective medium theories for nanoporous media, set the groundwork for analysis of the experimentally measured elastic properties of fluid-saturated nanoporous materials.

Experimental method for the determination of adsorption-induced changes of pressure and surface stress in nanopores

The change of surface stress is an important quantity characterising the behaviour of nanoporous systems, however, it is difficult to assess experimentally. In this letter we develop and demonstrate an experimental method for the determination of adsorption-induced changes of the surface stress in nanoporous materials. With the aid of ultrasonic measurements we determine the dependence of the adsorbate's longitudinal modulus [Formula: see text] on the adsorption-induced normal pressure, [Formula: see text], which is exerted by the adsorbate on the porous matrix. From this dependence we deduce the normal pressure at saturation, [Formula: see text], and thereby changes of the surface stress [Formula: see text] at the interface between the solid matrix and the liquid adsorbate. For the model system of argon in nanoporous glass (pore radius [Formula: see text] nm) the ultrasonic method reveals a value for [Formula: see text] that is in very good agreement with the theoretical value known for the argon-silica interface. The disclosure of this experimental method and its application on other systems will enable a better understanding of the behaviour of adsorbates in nanoporous materials.

Modulus-pressure equation for confined fluids

Ultrasonic experiments allow one to measure the elastic modulus of bulk solid or fluid samples. Recently such experiments have been carried out on fluid-saturated nanoporous glass to probe the modulus of a confined fluid. In our previous work [G. Y. Gor et al., J. Chem. Phys., 143, 194506 (2015)], using Monte Carlo simulations we showed that the elastic modulus K of a fluid confined in a mesopore is a function of the pore size. Here we focus on the modulus-pressure dependence K(P), which is linear for bulk materials, a relation known as the Tait-Murnaghan equation. Using transition-matrix Monte Carlo simulations we calculated the elastic modulus of bulk argon as a function of pressure and argon confined in silica mesopores as a function of Laplace pressure. Our calculations show that while the elastic modulus is strongly affected by confinement and temperature, the slope of the modulus versus pressure is not. Moreover, the calculated slope is in a good agreement with the reference data for bulk argon and experimental data for confined argon derived from ultrasonic experiments. We propose to use the value of the slope of K(P) to estimate the elastic moduli of an unknown porous medium.

Correlation between the Sorption-Induced Deformation of Nanoporous Glass and the Continuous Freezing of Adsorbed Argon

In this article we study the dependence of the sorption-induced deformation of nanoporous glass on the liquid-solid phase transition of adsorbed argon. During cooling we observe a continuous reduction of the expansion of the porous glass matrix caused by the adsorbate. The contraction is attended by a likewise continuous change of the adsorbed argon's phase state from liquid to solid. This simultaneous behavior evidences that the liquid-solid phase transition leads to a reduction of the pressure the adsorbate exerts on the pore walls. Furthermore, the study shows that small temperature changes can temporarily cause strong deformations of the porous material that decay in long time intervals of up to 1 week. We expect that our observations for the model system of argon and porous glass can be generalized to other systems. Consequently, this study will have implications when considering porous materials for applications, e.g., as a medium for storage.

Formation of Periodically Arranged Nanobubbles in Mesopores: Capillary Bridge Formation and Cavitation during Sorption and Solidification in an Hierarchical Porous SBA-15 Matrix

We report synchrotron-based small-angle X-ray scattering experiments on a template-grown porous silica matrix (Santa Barbara Amorphous-15) upon in situ sorption of fluorinated pentane C5F12 along with volumetric gas sorption isotherm measurements. Within the mean-field model of Saam and Cole for vapor condensation in cylindrical pores, a nitrogen and C5F12 sorption isotherm is well described by a bimodal pore radius distribution dominated by meso- and micropores with 3.4 and 1.6 nm mean radius, respectively. In the scattering experiments, two different periodicities become evident. One of them (d1 = 11.5 nm) reflects the next nearest neighbor distance in a 2D-hexagonal lattice of tubular mesopores. A second periodicity (d2 = 11.4 nm) found during in situ sorption and freezing experiments is traced back to a superstructure along the cylindrical mesopores. It is compatible with periodic pore corrugations found in electron tomograms of empty SBA-15 by Gommes et al. ( Chem. Mater. 2009, 21, 1311 - 1317). A Rayleigh-Plateau instability occurring at the cylindrical blockcopolymer micelles characteristic of the SBA-15 templating process quantitatively accounts for the superstructure and thus the spatial periodicity of the pore wall corrugation. The consequences of this peculiar morphological feature on the spatial arrangement of C5F12, in particular the formation of periodically arranged nanobubbles (or voids) upon adsorption, desorption, and freezing of liquids, are discussed in terms of capillary bridge formation and cavitation in tubular but periodically corrugated pores.

Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress

Adsorption-induced deformation has to be described in terms of the change of the surface stress Δfand not the surface energy Δγ. The former explains both expansion and contraction.