Effects of neutral solvent addition on the body-centered cubic spheres of block copolymers

We employ self-consistent mean-field (SCMF) theory in studying the body-centered cubic (bcc) spheres of block copolymers in the presence of a neutral solvent. First we examine the accuracy of the dilution approximation then analyze the dependence of the bcc structural sizes with copolymer volume fraction ϕ, the interaction parameter χAB, and degree of copolymerization N. Our results reveal that both distribution of each component and the micro-structural length scales are greatly influenced by each parameter ϕ, χAB, and N. As expected, with decreasing ϕ, more solvent distributes non-uniformally in the segregated domains, therefore deviation from the dilution approximation increases. This also suggests that when the effective segregation parameter ϕχABN is fixed, a larger deviation is expected as χABN increases (i.e. ϕ decreases). Although when both χABN and ϕ are fixed, decreasing N (i.e. increasing χAB) enlarges the deviation from the dilution approximation. Furthermore, this solvent non-uniformity behavior is so significant that it even affects the dependence of the domain spacing L* and the matrix length Λ* with respect to (χAB)effN=ϕχABN near the ODT. When the systems are in molten state and/or in the concentrated regime, both L* and Λ* exhibit a sharp increase behavior as ODT is approached, due to many of the minority blocks being pulled from the spherical domains and swelling the matrix. With increasing solvent amount and/or χABN, we observe that the increase of the degree for the minority blocks pulled from the spheres into the matrix near the ODT is not as significant as that in the melt. As such, the sharp increase behavior in L* as well as Λ* near the ODT smoothens and even disappears.