Three-dimensional structural analysis as a "new wave" in polymer physics - Geometrical features of phase-separated bicontinuous structures in a polymer blend studied by three dimensional microscopy

Three-dimensional (3D) structural analysis, which involves 3D image reconstruction and quantitative 3D measurements, is proposed as a new methodology in polymer physics. As an example of the application of the method, a phase-separated structure of a binary polymer blend undergoing late stage spinodal decomposition (SD) is discussed. Interface developed in the late stage SD (spinodal interface) was quantitatively observed in the 3D real space by using laser scanning confocal microscopy. The phase-separated structure was periodic and consisted of two independent interpenetrating-network (bicontinuous structure). Two novel methods were developed in order to numerically determine local curvatures, i.e., the mean and Gaussian curvatures, of the interface from the 3D reconstructed images. These methods are strictly based on the differential geometry. Joint probability densities of the local curvatures, i.e., the mean and Gaussian curvatures, of the spinodal interface have been experimentally evaluated for the first time. We found that a large portion of the interface formed in the late stage SD consists of a saddle-shaped surface, i.e., a hyperbolic surface. The probability densities of the curvatures obtained at various times were successfully scaled by a characteristic wave number, i.e., interface area per unit volume. This clearly proves that the time-evolution of the spinodal interface, which characterizes the local structure of the system, is dynamically self-similar. Besides the curvature measurement presented in this study, several parameters characterizing structures are proposed. They are, for example in the case of the bicontinuous structures, spatial distribution of vertices, length between the vertices, channel number at the vertices, etc. On application of these parameters, their measurements would settle down a controversial issue in characterization of bicontinuous structures in block copolymers. We also note that such parameters will not be obtained from another method except for the 3D structural analysis.