Isostatic Elasticity in a Biomolecular Network

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

This research program will investigate how the mechanical properties of soft, networked materials arise from the nanoscale structure and stiffness of their junctions and strands. Soft, networked materials are ubiquitous in biology and technology; examples include the cytoskeleton of living cells, elastomers, and hydrogels. Historically, the dominant model for explaining these materials' mechanical properties was the rubber model of elasticity. This model views network strands as entropic springs and predicts that the material's stiffness depends only on strand concentration and temperature—notably, it does not take any other aspect of network structure into account. However, classical mechanics tells us that the rigidity of a macroscopic network is strongly affected by the network's valence (the number of beams emanating from a joint). This insight, formalized by Maxwell, is known as the isostatic criterion: Networks of rigid beams connected by pin joints, at which beams freely rotate, must have a valence of 6 or more to be rigid, while networks of lower valence are floppy. By investigating how (valence-independent) rubber elasticity and (valence-dependent) isostaticity interact to create a soft, networked material's key mechanical properties, like deformability and failure, this work will produce a precision data set that will catalyze the development of constitutive models of isostatic deformation and failure, thus enabling rational prediction of material behavior in an engineering context. This research is imbued with a strong educational component: research projects will be offered to undergraduates for summer internships and research results will be integrated into classroom teaching. These activities, along with the involvement of graduate students, ensure that the project will significantly contribute to training the next generation of researchers in this growing field. The specific goal of the research is to discover the relationship by which junction valence, rotational freedom, and strand stiffness determine both linear and non-linear network mechanics. This will be pursued experimentally by rheological measurements of nanoscopically-defined networked materials formed from self-assembled DNA particles. The use of DNA offers (i) diminished entropic effects due to DNA’s semi-rigid structure; (ii) design control over joint and strand structure via DNA hybridization; and, (iii) dynamic control of the same via light-switchable moieties that alter the local stability of DNA hybridization. This project will advance the knowledge base at the intersection of mechanical engineering and material science and demonstrate unprecedented access to and control over the extreme mechanical properties enabled in networked materials. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.