The order-disorder and order-order transitions (ODT and OOT) in the linear multiblock copolymers with two-length scale architecture A(fmN)(B(N2)A(N2))(n)B((1-f)mN) are studied under intermediate cooling below the ODT critical point where a nonconventional sequence of the OOTs was predicted previously [Smirnova et al., J. Chem. Phys. 124, 054907 (2006)] within the weak segregation theory (WST). To describe the ordered morphologies appearing in block copolymers (BCs) under cooling, we use the pseudospectral version of the self-consistent field theory (SCFT) with some modifications providing a good convergence speed and a high precision of the solution due to using the Ng iterations [J. Chem. Phys. 61, 2680 (1974)] and a reasonable choice of the predefined symmetries of the computation cell as well as initial guess for the iterations. The WST predicted sequence of the phase transitions is found to hold if the tails of the BCs under consideration are symmetric enough (mid R:0.5-fmid R:0.05, a large region of the face-centered cubic phase stability is found (up to our knowledge, first within the SCFT framework) inside of the body-centered cubic phase stability region. Occurrence of the two-dimensional and three-dimensional phases with the micelles formed, unlike the conventional diblock copolymers, by the longer (rather than shorter) tails, and its relationship to the BC architecture is first described in detail. The calculated spectra of the ordered phases show that nonmonotonous temperature dependence of the secondary peak scattering intensities accompanied by their vanishing and reappearance is rather a rule than exception.

We present a statistical mechanical model, which is used to investigate the adsorption behavior of two-letter (AB) copolymers on chemically heterogeneous surfaces. The surfaces with regularly distributed stripes of two types (A and B) and periodic multiblock copolymers (Al)B(l))(x) are studied. It is assumed that A(B)-type segments selectively adsorb onto A(B)-type stripes. It is shown that the adsorption strongly depends on the copolymer sequence distribution and the arrangement of selectively adsorbing regions on the surface. The polymer-surface binding proceeds as a two-step process. At the first step, the copolymer having short blocks adsorbs onto the surface as an effective homopolymer, which does not feel chemical pattern. At the second step, when the polymer-surface attraction is sufficiently strong, the adsorbed chain adjusts its equilibrium conformation to reach the perfect bound state, thereby demonstrating ability for pattern recognition. The key element of this mechanism is the redistribution of strongly adsorbed copolymer diblocks A(l)B(l), which behave as surfactants, between multiple AB interfaces separating A and B stripes on the adsorbing surface. Such redistribution is accompanied by a well-pronounced decrease in the system entropy. We have found that marked pattern recognition is possible for copolymers with relatively short blocks at high polymer/surface affinities, beyond the adsorption threshold.

We present a statistical mechanical approach for predicting the self-assembled morphologies of amphiphilic diblock copolymers in the melt. We introduce two conformationally asymmetric linear copolymer models with a local structural asymmetry, one of a ''comb-tail'' type and another that we call ''continuous jackknife model.'' The copolymers consist of amphiphilic and ''monophilic'' (nonamphiphilic) blocks, which have different segmental volume and tend to segregate into subphases. Using a self-consistent field theory (SCFT) framework, we explore the phase diagrams for these copolymers and compare them with that known for conventional, conformationally symmetric diblock copolymers. To determine the impact of structural effects on the self-assembly of copolymer melts, copolymers with a variation in both molecular architecture and chemical composition, f, are studied for different values of the Flory-Huggins parameter, c. The composition dependence of the phase diagrams is shown to be basically determined by the conformational asymmetry. Remarkably, the stable lamellar structures exist even in the very compositionally asymmetric case, f < ¼. An interesting geometric distinction of the ''direct'' and ''inverse'' morphologies is introduced. The presence of an internal structure is found to influence the high c behavior, where a stable two-scale (structure-instructure) hexagonal morphology is found to be formed for some compositions. Therefore, the local chemical structure of monomer units can dictate the global morphology of copolymer melts.

We revisit the idea of the existence of the ordered block copolymer phase possessing diamond symmetry Fd 3m (space group No. 227), which was first put forward within the framework of the strong segregation approach. For this purpose we study the order-disorder and order-order transitions in molten two-scale multiblock copolymers A mN/2 (B N/2 A N/2) n B mN/2 via the pseudo-spectral numerical procedure of the self-consistent field theory (SCFT). The phase diagram in the plane (f C ,c), where f C ¼ n/(m + n) andc ¼ c N(m + n) is the effective energetic Flory-Huggins parameter, is built and some accompanying quantities are analyzed. Near the order-disorder transition line the phase diagram contains the regions where the lamellar, alternating gyroid, diamond and simple cubic phase, respectively, exist. With an increase of the degree of segregation, the diamond phase is replaced by a tetragonal array of cylinders (simple square) phase, which agrees with the preceding results obtained within the Leibler-like weak segregation theory, and with the SCFT calculations for a physically similar melt of linear ABC triblock copolymers with a non-selective middle block. Thus, the diamond morphology in the system under study is shown to exist as an essentially weak or moderately (not strongly) segregated phase. The ways to visualize the patterns of ordering in such morphologies are discussed. A new quantity (topological permeability) to characterize the transport properties in 3D bicontinuous morphologies is introduced and first calculated for real block copolymer ordered morphologies. Some implications of the results obtained for the design of the block copolymer thin films with improved permeability are discussed.

A new promising class of ordered block copolymer morphologies in thin films we call diamond-like morphologies (DLM) is theoretically described in detail. This class comprises the cubic morphologies possessing diamond symmetry Fd3̅m as well as its tetragonal and orthorhombic generalizations. The characteristic property of the DLM is that the corresponding percolation cluster contains both perpendicular and parallel (with respect to the substrate) intertwining channels, which is expected to improve noticeably the permeability efficiency of such quasi-isotropic morphologies as compared to the anisotropic lamellar and cylindrical ones. On the basis of both the weak segregation theory (WST) analytical consideration and self-consistent field theory (SCFT) numerical procedure, we find relationships between the microscopic parameters of the ternary ABC symmetric block copolymers of a specified composition and their morphology in thin films. The effects of confinement (film width) and the film walls selectivity are analyzed, and the corresponding phase diagrams are built. Our key theoretical prediction is that the way the selectivity is distributed over the film substrate makes a drastic difference in the selectivity influence on the various phases’ stability. The homogeneous selectivity distribution enhances the parallel lamellae stability. On the contrary, a simple 1D (lamellar) selectivity modulation could (depending on the modulation period) enhance the DLM stability. The explicit recommendations are made how to facilitate the DLM stabilizing in real block copolymers. We address also the issue of spectral and 3D visual ways to identify the SCFT equations solutions in thin films as the DLM.