An experimental test for effective medium approximations (EMAs)

Abstract

Aims. The effective medium approximations (EMAs), or the Lorentz–Lorenz, Maxwell-Garnett, and Bruggeman models, largely used to obtain optical properties and porosities of pure and ice mixtures, have been experimentally tested in this work. The efficiency of these approximations has been studied by obtaining the porosity value for carbon dioxide ice grown at low temperatures. An explanation of the behaviour of the experimental results for all temperatures is given. The analysis carried out for CO2 can be applied to other molecules. Methods. An optical laser interference technique was carried out using two laser beams falling on a growing film of ice at different incident angles which allowed us to determine the refractive index and the thickness of the film. The mass deposited is recorded by means of a quartz crystal microbalance. Porosity is determined from its equational definition by using the experimental density previously obtained. Results. From the experimental results of the refractive index and density, porosity values for carbon dioxide ice films grown on a cold surface at different temperatures of deposition have been calculated and compared with the results obtained from the EMA equations, and with recent experimental results. Conclusion. The values of porosity obtained with the EMA models and experimentally, show similar trends. However, theoretical values overestimate the experimental results. We can conclude that using the EMAs to obtain this parameter from an ice mixture must be carefully considered and, if possible, an alternative experimental procedure that allows comparisons to be made should be used.

Porosimetry for Thin Films of Metal–Organic Frameworks: A Comparison of Positron Annihilation Lifetime Spectroscopy and Adsorption‐Based Methods

“…and Bruggeman EMA equations are commonly applied to process EP data. [96,[101][102][103] These EMAs allow plotting the quantity adsorbed as a function of the relative pressure, instead of merely the refractive index or Ψ-Δ raw data. If the refractive index or Ψ-Δ raw data are plotted, it is conventional to do so at 633 nm, the operating wavelength of HeNe laser ellipsometers.…”

Atomic-Layer-Deposited SiOx/SnOx Nanolaminate Structure for Moisture and Hydrogen Gas Diffusion Barriers

“…The method of calculating porosity from refractive index has been calculated through a measurement method called ‘ellipsometric porosimetry’, theoretically based on effective medium approximations (EMA) . The Maxwell–Garnett, Bruggeman, and Lorentz–Lorenz methods were derived based on different assumptions . The most commonly used Lorentz–Lorenz equation is as follows Here, n f , n b , and p are the refractive index of the film material, refractive index of the bulk material without voids (2.0 for SnO 2 bulk), and porosity, respectively.…”

Ultrasonic Propagation in Liquid and Ice Water Drops. Effect of Porosity

“…This leads to a fluffy cometary ice structure since comets are made by agglomeration of icy dust particles [1,2]. The porosity values in such ice analogs measured in the laboratory can be up to 40% for H 2 O and CO 2 ice [3,4] or up to 80% in water ice grown by vapor deposition at large incident angles [5].…”