Optical porosimetry of weakly absorbing porous materials.

Quentin Libois,Félix Lévesque-Desrosiers,Simon Lambert-Girard,Florent Domine,Simon Thibault

doi:10.1364/oe.27.022983

Abstract

The physical porosity ${\Phi}$Φ of a porous material determines most of its properties. Although the optical porosity ${\Phi} _{\textrm {opt}}$Φopt can be measured, relating this quantity to ${\Phi}$Φ remains a challenge. Here we derive relationships between the optical porosity, the effective refractive index $n_{\textrm {eff}}$neff and the physical porosity of weakly absorbing porous media. It introduces the absorption enhancement parameter ${B}$B, which quantifies the asymmetry of photon path lengths between the solid material and the pores and can be derived from the absorption coefficient $\mu _a$μa of the material. Hence ${\Phi}$Φ can be derived from combined measurements of $n_{\textrm {eff}}$neff and $\mu _a$μa. The theory is validated against laboratory measurements and numerical experiments, thus solving a long-standing issue in optical porosimetry. This suggests that optical measurements can be used to estimate physical porosity with an accuracy better than 10$\%$%.

Highlights

Porosity controls the mechanical [1], radiative [2], thermal [3], chemical [4] and acoustic [5] properties of porous materials
We show that the lengthening of photon paths in the phase with greater refractive index, which results from internal multiple scattering in this phase, is directly related to the bulk absorption coefficient μa of the medium, as long as absorption only occurs in this phase and remains weak, which is often the case
We presented a method to determine the porosity of a weakly absorbing porous material using optical measurements

Summary

Introduction

Porosity controls the mechanical [1], radiative [2], thermal [3], chemical [4] and acoustic [5] properties of porous materials. The extinction coefficient μe of a medium only depends on its density and specific surface area which are purely geometrical quantities [11], most optical measurements can only provide the absorption coefficient μa and reduced scattering coefficient μs = (1 − g)μs, with μe = μa + μs, μs being the scattering coefficient. This highlights the contribution of the generally unknown phase function of the medium through the asymmetry parameter g [12,13]

Objectives

Findings

Discussion

Conclusion