Direct measurement of interface anisotropy of bicontinuous structures via 3D image analysis

A very important morphological parameter in two-phase fluids is the interface anisotropy, which can be quantified using the interface tensor, q(ij). However, the computation of this tensor for complex interfaces is not straightforward. A novel method (the local cross product method, LCPM) to compute the interface tensor of two-phase fluids using 3D imaging coupled with differential geometry is presented here. The method was used to evaluate the degree of anisotropy of phase separated systems with bicontinuous morphologies subjected to uniaxial and shear deformation fields. A model bicontinuous structure (i.e., the gyroid surface) was used to assess the accuracy and precision of the method. The method was then used to track the anisotropy changes of an immiscible polymer blend with cocontinuous morphology, during uniaxial deformation and subsequent retraction. It was found that the dependence of the anisotropy on the Hencky strain of both the gyroid surface and the cocontinuous blend follow the same trend. The retraction of the blend after uniaxial extension is accompanied by an exponential decay of the second invariant of q(ij), which obeys the relation: |II(q)|/Q(2) approximately e(-0.129t).