We formulate a viscoelastic theory for interconnected microphase separated structures such as a double gyroid in diblock copolymer melts. We consider the energy increase and the energy dissipation due to the deformation of interconnected periodic domains. The dominant elastic part agrees with previous analytical results obtained by a phase formulation of deformations. It is shown that a viscous...

The effect of A-block polydispersity on the phase behavior of AB-diblock copolymer melts is examined using a complete self-consistent field theory treatment that allows for fractionation of the parent molecular-weight distribution. In addition to observing the established shift in phase boundaries, we find the emergence of significant two-phase coexistence regions causing, for instance, the dis...

We propose a fast and robust scheme for the direct minimization of Ohta-Kawasaki energy that characterizes microphase separation diblock copolymer melts. The employs globally convergent modified Newton method with line search which is shown to be mass-conservative, energy-descending, asymptotically quadratically convergent, three orders magnitude more efficient than commonly-used gradient flow ...

A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P,D, gyroid and H surfaces. Some of these graphs are natural ge...

Block copolymers spontaneously self-assemble into well defined structures with variable geometry (spherical, cylindrical, lamellar etc) depending on the chemical details (molecular structure, composition etc) and external conditions such as temperature and pressure. It is of significant interest to understand how this structure formation, typical in the range of some tenths to hundreds of nanom...

We study analytically the intricate phase behavior of cross-linked AB diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints. Gelation, i.e., spatially random localisation of polymers forming a system-spanning cluster, is driven by increasing the number parameter μ of irreversible, type-selective cross-links between random pairs of A blocks. Sel...

– We consider microand macro-phase separation in blends of AB and BC flexible diblock copolymers. We show that, depending on architecture, a number of phase diagram topologies are possible. Microphase separation or macrophase separation can occur, and there are a variety of possible Lifshitz points. Because of the rich parameter space, Lifshitz points of multiple order are possible. We demonstr...