Continuous and discontinuous transitions between double primitive network and body-centered cubic spheres.

A stable region of the double primitive (DP) network structure formed by the AB-type comb-shaped block copolymer (A-g-B CSBCP) melts is identified using self-consistent field theory. The formation mechanism of the DP network is systematically investigated. In the mean-field limit, the transition in the A-g-B CSBCP melts between the DP network and its spherical counterpart, the metastable body-centered cubic (BCC) spheres, can be either continuous or discontinuous, distinct from the typical order-order transitions (OOTs) observed in conventional block copolymer melts. We further determine the critical point at which the discontinuity vanishes. Our results demonstrate that the stability of the DP phase and the continuous OOT primarily originate from the unique chain architecture of the A-g-B CSBCP.