TRIPLY PERIODIC LEVEL SURFACES AS MODELS FOR CUBIC TRICONTINUOUS BLOCK-COPOLYMER MORPHOLOGIES

The domains of microphase separated block copolymers develop interfaci al surfaces of approximately constant mean curvature in response to th ermodynamic driving forces. Of particular recent interest are the tric ontinuous triply periodic morphologies and their mathematical represen tations. Level surfaces are represented by certain real functions whic h satisfy the expression F(x,y,z) = t, where t is a constant. In gener al, they are non-self-intersecting and smooth, except at special value s of the parameter t. We construct periodic level surfaces according t o the allowed reflections of a particular cubic space group; such trip ly periodic surfaces maintain the symmetries of the chosen space group and make attractive approximations to certain recently computed tripl y periodic surfaces of constant mean curvature. This paper is a study of the accuracy of the approximations constructed using the lowest Fou rier term of the <Pm(3)over bar m>, <Fd(3)over bar m> and I4(1)32 spac e groups: and the usefulness of these approximations in analysing expe rimentally observed tricontinuous block copolymer morphologies at a va riety of volume fractions. We numerically compare surface area per uni t volume of particular level surfaces with constant mean curvature sur faces having the same volume fraction. We also demonstrate the utility of level surfaces in simulating projections of tricontinuous microdom ain morphologies for comparison with actual transmission electron micr ographs and determination of block copolymer microstructure.