Measurement of geometrical parameters in cocontinuous polymer blends: 3D versus 2D image analysis

Formulae of stereology are used to estimate 3D geometrical parameters of cocontinuous structures measured from 2D micrographs of polymer blends. 3D images of symmetric and nonsymmetric polymer blends made of fluorescently labelled polystyrene and styrene-ran-acrylonitrile copolymer were obtained with laser scanning confocal microscopy. Geometrical parameters of the blend interface, specifically volume fraction, surface area per unit volume (S_V) and average of local mean curvature were measured directly from the 3D images and compared to the values estimated from analysis of a number of 2D slices combined with stereological relations. When the total length of phase boundary considered in the analysis of the 2D slices (L_Tot) was at least 6000 times bigger than the characteristic length of the microstructure (S^-1_V), the standard deviation for all the parameters measured became negligible. However, considerable discrepancies between the average values computed from 3D and 2D images were observed for any value of L_Tot. The mean curvature distribution was also measured from both the 3D images and the 2D slices. The distribution was estimated from the 2D slices but with a width about 2.4 times that of the true value obtained from the 3D images.