Copolymer-homopolymer blends: global energy minimisation and global energy bounds
نویسندگان
چکیده
We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points. Furthermore we characterise the conditions under which the minimisers may be non-unique. In higher dimensions we construct lower and upper bounds on the energy of minimisers, and explicitly compute the energy of spherically symmetric configurations.
منابع مشابه
Effect of homopolymer molecular weight on order-order transition in block copolymer and homopolymer blends.
The order-order transition temperature (T(OOT)) in blends of poly(styrene-b-isoprene-b-styrene) (S-I-S) triblock copolymer and polyisoprene (PI) homopolymer was investigated by using synchrotron small-angle X-ray scattering (SAXS). Pure triblock copolymer undergoes an order-order transition (OOT) from hexagonally ordered cylinder (HEX) to body centered cubic (BCC) phases. In order to investigat...
متن کاملDiblock Copolymer / Homopolymer Blends: Derivation of a Density Functional Theory
Melts of diblock copolymer / homopolymer blends exhibit multiscale phase separation: (i) macrophase separation into homopolymerand copolymer-rich macrodomains followed by (ii) microphase separation into Aand B-rich microdomains within the copolymer-rich macrodomains (cf. [16, 17, 26]). Following our previous derivation in [6], we derive a density functional theory for blends. This theory has be...
متن کاملTricontinuous cubic structures in ABC/A/C copolymer and homopolymer blends.
Using the Monte Carlo lattice-simulation technique, we present numerical evidence of the formation of gyroid and nongyroid tricontinuous cubic phases in high polymeric systems of ABC/A/C triblock copolymer and homopolymer blends. By increasing the volume fraction of homopolymer, a remarkable phase sequence G (gyroid) --> D (diamond) --> P (primitive) is observed, which is common to certain surf...
متن کاملSelf-assembled Nanostructures in Copolymer Blends: Saxs, sans and Tem Study
Phenomena associated with the phase behaviour and self-assembled nanostructures of three block copolymer systems have been studied by small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS) and transmision electron microscopy (TEM). 1) System A-b-B/A (dPS-b-PMMA/PS homopolymer) were studied as a function of molecular weight and concentration of the added homopolymer. The para...
متن کاملLifshitz points in blends of AB and BC diblock copolymers
– 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...
متن کامل