Self-Consistent Field Approach for Cross-Linked Copolymer Materials

Abstract

A generalized self-consistent field approach for polymer networks with fixed topology is developed. It is shown that the theory reproduces the localization of crosslinks which is characteristic for gels. The theory is then used to study the order-disorder transition in regular networks of endlinked diblock copolymers. Compared to diblock copolymer melts, the transition is shifted towards lower values of the incompatibility parameter χ (the Flory-Huggins parameter). Moreover, the transition becomes strongly first order already at the mean-field level. If stress is applied, the transition is further shifted and finally vanishes in a critical point.PACS numbers: 64.70. Nd, 64.75.Nd, 6.25.hp, 47.57.jb Polymers are macromolecules made of a large number of structurally identical or similar subunits (monomers), with local monomer interactions that tend to be weak on the scale of the thermal energy k B T . In polymeric materials, molecules typically have many interaction partners. Therefore, these systems can often be described quite satisfactorily by mean field theories. In particular, the self-consistent field (SCF) theory [1-6] is a powerful mean field approach for describing inhomogeneous polymer melts and solutions. Originally developed as a theory for interfaces between immiscible homopolymer phases [1], it has by now become a standard tool for studying phase transitions between block copolymer mesophases [7][8][9], the self-organization of amphiphilic polymers in solution [10], or the structure of polymer composite materials [11][12][13], to name just a few examples. Numerous extensions have been proposed that allow one to include, e.g., orientational order [14], electrostatic interactions [15], dynamical processes [16][17][18][19] or the effect of fluctuations [20][21][22].Despite these successes, the SCF theory still suffers from severe restrictions. Most prominently, it is limited to fluids. Polymers are taken to have full translational freedom and, consequently, the systems cannot sustain large shear stress or elastic deformations. Complex fluids may respond elastically to small stress to some extent, and this can be studied by SCF methods [23,24], but they necessarily yield to large stress. In reality, however, many materials of interest such as rubber are irreversibly crosslinked, either chemically or physically. Crosslinking is a popular strategy for stabilizing composite materials or polymeric nanostructures. While SCF approaches have been devised for describing systems of reversibly crosslinked polymeric materials [25][26][27], there exists so far no SCF theory for irreversibly crosslinked polymer networks.In the present paper, we propose a way to overcome this limitation. We develop a SCF approach for irreversibly crosslinked networks with fixed (quenched) topology.As an application example, we then use the method to study the phase behavior of symmetric cross-linked diblock copolymers. Specifically, we address the question how crosslinking affects the order-disorder transition (ODT), i.e., the trans...

Model Amphiphilic Polymer Conetworks in Water: Prediction of Their Ability for Oil Solubilization

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