Measurements of interfacial curvatures of bicontinuous structure from three-dimensional digital images. 1. A parallel surface method

A method was developed to measure the area-averaged mean and the Gaussian curvatures from three-dimensional (3D) digital images of the interface of complicated bicontinuous structures. This method involves measurement of areas of surfaces that are parallel to the interface as a function of displacement from it. The applicability and precision of the scheme were critically examined by using a known minimal surface, i.e., the gyroid, as a model of bicontinuous structures. The method was then applied to 3D images of the interface of the phase-separated bicontinuous structure of a real polymer blend in order to evaluate the characteristic of curvatures of the interface.