Digital image analysis of droplet patterns in polymer systems: Point pattern

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Abstract
New techniques of digital image analysis which are especially suitable for analyzing particle-distribution patterns are presented. Statistical mathematical methods are applied to the quantitative analysis of a spatial distribution of points in polymer systems. The techniques are useful for studying the spatial patterns of particles or droplets which are commonly observed in nucleation-growth-type phase separation and late-stage spinodal decomposition in polymer mixtures, crystallization process, microphase separation in block copolymers, incompatible polymer alloys, and composite materials, etc. We can divide point patterns into three typical point patterns: the Poisson pattern, the clustered pattern, and the regular pattern. The kind and strength of interaction or force between points can be determined from spatial point-distribution patterns. The point-pattern analysis has been applied to phase-separated structures of a polymer mixture, and it has been revealed that the pattern belongs to the regular pattern. The appearance of the regular pattern is probably a result of the Brownian coalescence mechanism for the droplet growth and it might also be due to a long-range interaction among droplets through diffusion field.