An Image Analysis Method for Cell-Size and Cell-Size Distribution Measurement in Rigid Foams

Abstract

The basic morphological unit of a closed cell rigid foam is the gas-filled cavity surrounded by cell walls and struts. Typically, these cavities (cells) are pentagonal dodecahedral or tetrakaidecahedral. Their average dimensions and dispersity are known to influence foam physical properties and foam performance. We have devised a reliable method for the measurement of cell-size and cell-size distribution which exploits both geometry and statistics, and which has allowed the realization of useful correlations and trends in our development of rigid foam formulations and additives. A thin slice of foam (100-300 microns) is subjected to optical microscopy and image analysis. Measurements of the areas of cell windows and of the average ferets of these windows are made independently. Windows are usually pentagonal, hexagonal or square and are variously distorted. Cells are assumed to be dodecahedral and cell diameter ( d) is calculated by the formulae: d = 2.1354 (area)1/2 d = 1.7013 (feret) Thereby, two independent determinations of cell diameter are obtained from each window viewed. Values are typically within 2% of each other. Cell-size distribution is quantified by measuring a large number (~ 500-1000) of windows and calculating the simple and weighted averages. This paper will present the mathematical basis for the method, illustrate the excellent agreement between the window area and the feret cell-size determinations and demonstrate the utility of cell-size and cell-size distribution data in physical property correlations, for example for k-factor.