Morphology of nanoporous glass: Stochastic 3D modeling, stereology and the influence of pore width

Abstract

Excursion sets of Gaussian random fields are used to model the three-dimensional (3D) morphology of differently manufactured porous glasses (PGs), which vary with respect to their mean pore widths measured by mercury intrusion porosimetry. The stochastic 3D model is calibrated by means of volume fractions and two-point coverage probability functions estimated from tomographic image data. Model validation is performed by comparing model realizations and image data in terms of morphological descriptors which are not used for model fitting. For this purpose, we consider mean geodesic tortuosity and constrictivity of the pore space, quantifying the length of the shortest transportation paths and the strength of bottleneck effects, respectively. Additionally, a stereological approach for parameter estimation is presented, i.e., the 3D model is calibrated using merely two-dimensional (2D) cross-sections of the 3D image data. Doing so, on average, a comparable goodness of fit is achieved as well. The variance of the calibrated model parameters is discussed, which is estimated on the basis of randomly chosen, individual 2D cross-sections. Moreover, interpolating between the model parameters calibrated to differently manufactured glasses enables the predictive simulation of virtual but realistic PGs with mean pore widths that have not yet been manufactured. The predictive power is demonstrated by means of cross-validation. Using the presented approach, relationships between parameters of the manufacturing process and descriptors of the resulting morphology of PGs are quantified, which opens possibilities for an efficient optimization of the underlying manufacturing process.