Examination of the Topological Constraints of Lamellae-Forming Block Copolymers


Topological constraints also called entanglements regulate the dynamics of every molecule in the melt. However, little is known about these topological constraints when micro-phase segregation comes into play. In the context of lithography, attention has to be focused on the capability to control the self-assembly and orientation of the nano-domains. Unfortunately, assembling the block copolymers into defect-free structures can be quite challenging. Therefore, given the potential relevance of such topological constraints on the ordering kinetics, it is critical to develop top-down approaches that are capable of incorporating the effects of topological interactions on coarse-grained polymer models. To this note, several scholars have already attempted to explore the capacity of one of the most auspicious approaches: the slip-spring models, to capture the main relaxation mechanisms of entangled polymers, but not all the relevant details have been captured.

Recently, Abelardo Ramírez-Hernández and colleagues investigated the structural information regarding topological constraints of phase separated block copolymers using a detailed model. Additionally, they also used the information obtained to evaluate the performance of a zeroth-order slip-spring representation of the same materials. Their work is currently published in the research journal, Macromolecules.

The research technique employed in their study mainly used microscopic molecular model of diblock copolymers to examine melts of polymerization degree N = 100 and N = 400. Next the researchers obtained the topological constraints for both N by using the Z1 algorithm.

The authors observed that the topological constraints were not homogeneously distributed but instead exhibited a non-uniform spatial localization as a consequence of the self-organization of the polymer blocks. In additions, the researchers noted that the specific shape of the inhomogeneous distribution was affected by the molecular weight, N. Moreover, a comparison of the microscopic information obtained from these calculations with the corresponding results generated by a direct implementation of the slip-spring model originally developed for homopolymers and thereby showing good agreement.

The study has examined how microphase segregation alters the distribution of topological constraints, both in space and along chain contours. The researchers have shown that the coarse-grained approach they employed is able to capture the leading correlation between entanglements and polymer density in micro-phase segregated, lamellar systems. Altogether, the work teach us that the slip-spring model can offer a reasonable description of the spatial organization of entanglements in ordered block copolymer systems and could therefore serve as the basis for studies of rheology in this class of materials.


Abelardo Ramírez-Hernandez, ́ Brandon L. Peters, Ludwig Schneider, Marat Andreev, Jay D. Schieber, Marcus Müller, Martin Kröger,  and Juan J. de Pablo. A Detailed Examination of the Topological Constraints of Lamellae-Forming Block Copolymers. Macromolecules 2018, volume 51, pages 2110−2124.

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