Bayesian estimation of pore size distribution in porous carbon using a novel GCMC-based kernel incorporating surface roughness

Estimation of pore size distribution using concentric double pulsed-field gradient NMR

Pulsed field gradient (PFG) diffusion NMR experiments are sensitive to restricted diffusion within porous media and can thus reveal essential microstructural information about the confining geometry. Optimal design methods of inverse problems are designed to select preferred experimental settings to improve parameter estimation quality. However, in pore size distribution (PSD) estimation using NMR methods as in other ill-posed problems, optimal design strategies and criteria are scarce. We formulate here a new optimization framework for ill-posed problems. This framework is suitable for optimizing PFG experiments for probing geometries that are solvable by the Multiple Correlation Function approach. The framework is based on a heuristic methodology designed to select experimental sets which balance between lowering the inherent ill-posedness and increasing the NMR signal intensity. This method also selects favorable discrete pore sizes used for PSD estimation. Numerical simulations performed demonstrate that using this framework greatly improves the sensitivity of PFG experimental sets to the pores' sizes. The optimization also sheds light on significant features of the preferred experimental sets. Increasing the gradient strength and varying multiple experimental parameters is found to be preferable for reducing the ill-posedness. We further evaluate the amount of pore size information that can be obtained by wisely selecting the duration of the diffusion and mixing times. Finally, we discuss the ramification of using single PFG or double PFG sequences for PSD estimation. In conclusion, the above optimization method can serve as a useful tool for experimenters interested in quantifying PSDs of different specimens. Moreover, the applicability of the suggested optimization framework extends far beyond the field of PSD estimation in diffusion NMR, and reaches design of sampling schemes of other ill-posed problems.

Standard pore size determination methods like mercury porosimetry, nitrogen sorption, microscopy, or X-ray tomography are not suited to highly porous, low density, and thus very fragile materials. For this kind of materials, a method based on thermal characterization has been developed in a previous study. This method has been used with air pressure varying from 10-1 to 105 Pa for materials having a thermal conductivity less than 0.05 W m-1 K-1 at atmospheric pressure. It enables the estimation of pore size distribution between 100 nm and 1 mm. In this paper, we present a new experimental device enabling thermal conductivity measurement under gas pressure up to 106 Pa, enabling the estimation of the volume fraction of pores having a 10 nm diameter. It is also demonstrated that the main thermal conductivity models (parallel, series, Maxwell, Bruggeman, self-consistent) lead to the same estimation of the pore size distribution as the extended parallel model (EPM) presented in this paper and then used to process the experimental data. Three materials with thermal conductivities at atmospheric pressure ranging from 0.014 W m-1 K-1 to 0.04 W m-1 K-1 are studied. The thermal conductivity measurement results obtained with the three materials are presented, and the corresponding pore size distributions between 10 nm and 1 mm are presented and discussed.

Reconstructing a pore size distribution of porous materials is valuable for applications in materials sciences, oil well logging, biology, and medicine. The major drawback of NMR based methods is an intrinsic limitation in the reconstruction which arises from the ill-conditioned nature of the pore size distribution problem. Consequently, while estimation of the average pore size was already demonstrated experimentally, reliable evaluation of pore size distribution remains a challenging task. In this paper we address this problem by analyzing the mathematical characteristics that create the difficulty and by proposing an NMR methodology and a numerical analysis. We demonstrate analytically that an accurate reconstruction of pore size distribution is problematic with the current known strategies for conducting a single or a double pulsed field gradient (s-PFG, d-PFG) experiment. We then present a method for choosing the experimental parameters that would significantly improve the estimation of the size distribution. We show that experimental variation of both q (the amplitude of the diffusion gradient) and ϕ (the relative angle between the gradient pairs) is significantly favorable over single and double-PFG applied with variation of only one parameter. Finally, we suggest a unified methodology (termed Concentric d-PFG) that defines a multidimensional approach where each data point in the experiment is characterized by ϕ and q. The addition of the angle parameter makes the experiment sensitive to small compartment sizes without the need to use strong gradients, thus making it feasible for in-vivo biological applications.

Bayesian Estimation of Pore Size Distribution in Porous Carbon Using a Novel Gcmc-Based Kernel Incorporating Surface Roughness

Nuclear magnetic relaxation in activated carbon—water and activated carbon—benzene adsorption systems was studied by pulse NMR methods. Activated carbons characterized by different porous structures and chemical state of the surface were used. The application of the three-pulse Goldman—Shen sequence to the adsorption system generates a dipole echo caused by the dipole-dipole coupling of “structural” protons, which is not averaged due to their mobility during experiment. The non-exponential character of relaxation attenuations of the transverse and longitudinal nuclear magnetizations of physically adsorbed molecules in activated carbon pores is a result of differencies in pore sizes. The pore sizes in activated carbon and the size distribution were determined from the data of nuclear magnetic relaxation with allowance for the contribution from the “structural” protons.

Improving estimation of pore size distribution to predict the soil water retention curve from its particle size distribution

Cobalt oxide silica membranes were prepared and tested to separate small molecular gases, such as He (dk = 2.6 Å) and H2 (dk = 2.89 Å), from other gases with larger kinetic diameters, such as CO2 (dk = 3.47 Å) and Ar (dk = 3.41 Å). In view of the amorphous nature of silica membranes, pore sizes are generally distributed in the ultra-microporous range. However, it is difficult to determine the pore size of silica derived membranes by conventional characterization methods, such as N2 physisorption-desorption or high-resolution electron microscopy. Therefore, this work endeavors to determine the pore size of the membranes based on transport phenomena and computer modelling. This was carried out by using the oscillator model and correlating with experimental results, such as gas permeance (i.e., normalized pressure flux), apparent activation energy for gas permeation. Based on the oscillator model, He and H2 can diffuse through constrictions narrower than their gas kinetic diameters at high temperatures, and this was possibly due to the high kinetic energy promoted by the increase in external temperature. It was interesting to observe changes in transport phenomena for the cobalt oxide doped membranes exposed to H2 at high temperatures up to 500 °C. This was attributed to the reduction of cobalt oxide, and this redox effect gave different apparent activation energy. The reduced membrane showed lower apparent activation energy and higher gas permeance than the oxidized membrane, due to the enlargement of pores. These results together with effective medium theory (EMT) suggest that the pore size distribution is changed and the peak of the distribution is slightly shifted to a larger value. Hence, this work showed for the first time that the oscillator model with EMT is a potential tool to determine the pore size of silica derived membranes from experimental gas permeation data.

Different structural porous ceramic filters were investigated by the nitrogen gas permeability through the filters which were immersed in ethanol bath. The proposed method can discriminate between symmetric and asymmetric pore structure from the nitrogen gas permeability, and further the pore size distributions can be calculated from the relationship between volumetric flow rate and pressure. The permeability of the symmetric filter can be described on the basis of the Hagen-Poiseuille equation and the calculated result of pore size distribution was in accordance with the data from the measurement using mercury penetration porosimetry. Also the pore size distribution ranges in the limit of pore size corresponding to the pressure in which the total permeable area increases remarkably. In the case of the asymmetric filter, a discontinuous point was shown in the relationship between exhaust pressure and volumetric velocity. It was shown that this discontinuity was due to the asymmetric pore structures. The asymmetric permeability was also described on the basis of the Hagen-Poiseuille equation. It was found from the comparison of the results between the gas and mercury penetration methods that the gas penetration method could be applied to the measurement of the pore size distribution of the skin part in the filter which indicated asymmetry.

Electrospinning process can fabricate nanomaterials with unique nanostructures for potential biomedical and environmental applications. However, the prediction and, consequently, the control of the porous structure of these materials has been impractical due to the complexity of the electrospinning process. In this research, a theoretical model for characterizing the porous structure of the electrospun nanofibrous network has been developed by combining the stochastic and stereological probability approaches. From consideration of number of fiber-to-fiber contacts in an electrospun nanofibrous assembly, geometrical and statistical theory relating morphological and structural parameters of the network to the characteristic dimensions of interfibers pores is provided. It has been shown that these properties are strongly influenced by the fiber diameter, porosity, and thickness of assembly. It is also demonstrated that at a given network porosity, increasing fiber diameter and thickness of the network reduces the characteristic dimensions of pores. It is also discussed that the role of fiber diameter and number of the layer in the assembly is dominant in controlling the pore size distribution of the networks. The theory has been validated experimentally and results compared with the existing theory to predict the pore size distribution of nanofiber mats. It is believed that the presented theory for estimation of pore size distribution is more realistic and useful for further studies of multilayer random nanofibrous assemblies.

\nPore size distribution is an important feature of granular materials in the context of filtration and erosion in soil hydraulic structures. Present study focuses on the evolution characteristics of pore size distribution for numerically simulated granular assemblies while subjected to various compression boundary constrain, namely, conventional drained triaxial compression, one-dimensional or oedometric compression and isotropic compression. We consider the effects initial packing of the granular assembly, loose or dense state. A simplified algorithm based on Delaunay tessellation is used for the estimation of pore size distribution for the deforming granular assemblies at various stress states. The analyses show that, the evolution of pore size is predominantly governed by the current porosity of the granular assembly while the stress path or loading process has minimal influence. Further it has also been observed that pore volume distribution reaches towards a critical distribution at the critical porosity during shear enhanced loading process irrespective of the deformation mechanism either compaction or dilation.\n

Pore size distribution is an important factor that affects the moisture diffusion and permeability properties of cement-based materials. For cement paste, it is assumed that the mesopores (100 nm–0.01 mm) and macropores (0.01 mm–1 cm) can be neglected compared to the micropores (<100 nm). Based on the surface energy theory, moisture chemical potential of pore water is introduced to explain the liquid-gas equilibrium in pores with different radius. Using chemical potential as an intermedium, a quantitative relationship between micropore size distribution and water adsorption isotherms can be established. The micropore size distribution can be treated as an explanation of the moisture adsorption behavior, and by using adsorption isotherms, the micropore size distribution can be estimated conveniently. Mortar and concrete can be regarded as a combination of cement paste and aggregates; thus, besides the micropores, the mesopores and macropores are also taken into consideration. Finally, the general empirical estimation equations for pore-size distribution are developed for cement, mortar, and concrete, which can be used for refined modeling and simulating of durability-related issues, such as frost action, water permeability, and drying shrinkage.

Reliable prediction of pore size distribution for nano-sized adsorbents with minimum information requirements

Characterization of pore structure in cement-based materials using pressurization–depressurization cycling mercury intrusion porosimetry (PDC-MIP)

Robust PSD determination of micro and meso-pore adsorbents via novel modified U curve method