Mechanical phase transitions and the rheology of stiff polymers

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NONTECHNICAL SUMMARYThis award supports theoretical and computational research and education on how collagen and fiber networks more generally respond to mechanical deformation. In animals, most soft tissues such as skin, tendon and organs depend on networks of collagen that impart mechanical stability to the full tissue. Similar networks of fibrinogen also form as part of the wound healing process. A common feature in the mechanical response of such natural biopolymer materials is that they become stronger, with increased mechanical stiffness as they are deformed. This self-stabilizing mechanical response is still not well understood and it has been difficult to achieve in man-made soft materials, such as rubber or other synthetic polymer-based materials. This project is aimed to develop a fundamental theoretical model and understanding of the mechanics of collagen and related biopolymer-based materials. This will be based on the fundamental physics of phase transitions or changes of state, much like the change of state of water to form solid ice as it is cooled. The PI and colleagues have recently demonstrated that collagen networks undergo a similar mechanical phase change as they are deformed rather than cooled. A fundamental understanding of the origins of the mechanical response of collagen and related fiber-based materials can be the basis for the rational design of synthetic materials with similar properties. This project can also form the theoretical basis for control and design of the mechanical properties of carbon nanotube foams and aerogels, which have recently emerged as a promising class of very light and soft conductors. The research in this project will be the basis for training of graduate students working at the interface between physics and chemical engineering, with application perspectives in tissue engineering and materials science. The research will also impact the teaching of mechanics of materials to undergraduates and graduate students working in chemical and biomolecular engineering, chemistry, physics and materials science at Rice University.TECHNICAL SUMMARYThis award supports theoretical and computational research on the mechanics and rheology of athermal fiber networks. Polymers naturally range from highly flexible or freely jointed chains to idealized rigid rods, with a broad class of semiflexible polymers in between that are often described as wormlike chains. The so-called persistence length, which characterizes the scale over which polymers appear straight in the presence of thermal fluctuations, is often used to distinguish these regimes. Among the most rigid of polymers are biopolymers that play important structural and mechanical roles from the single cell level to the whole tissue level of extracellular matrices. The principal component of extracellular matrices is usually collagen, consisting of thick protein fibers with effectively infinite persistence length and negligible thermal fluctuations. Nevertheless, collagen fibers are not rigid rods and bending plays an important role in the mechanical response of collagen networks. The challenge of understanding such networks has recently brought renewed interest to the mechanics and rheology of athermal fiber networks. A new approach to fiber networks has recently been proposed, drawing on the notion of athermal, mechanical phase transitions and associated critical phenomena. This was motivated in part by classic work on network stability going back to Maxwell's isostatic constraint counting arguments, as well as more recent developments in jamming of particles. Importantly, however, the isostatic threshold cannot account for the mechanics of real fiber networks in 3D, since these lie below the Maxwell point for central-force or spring-like interactions: bending must be included. The PI's group recently identified theoretically signatures of critical phenomena in subisostatic networks as a function of strain, which have now been confirmed experimentally in collagen networks. This project aims to (1) develop and test computationally scaling theories for mechanical phase transitions in fiber networks; (2) predict and test phase behavior and rheological signatures of strain-controlled phase transitions; (3) develop models of composite fiber networks, with both fluid and soft gel matrices; (4) develop computational models for carbon nanotube gels.This approach based on mechanical phase transitions and especially strain-controlled critical phenomena represent a novel approach to polymer rheology. This research will deepen our understanding of a class of mechanical phase behavior that should be of significant interest within condensed matter and materials science, while establishing fiber networks as new model systems in which to study critical phenomena using rheology.The study of composite networks should significantly advance the quantitative understanding of collagen extracellular matrices, for which a consensus theoretical model has been lacking. This project can also form the theoretical basis for control and design of the mechanical properties of carbon nanotube foams and aerogels, which have recently emerged as a class of very light and soft conductors. The research in this project will be the basis for training of graduate students working at the interface between physics and chemical engineering, with application perspectives in tissue engineering and materials science. The research will also impact the teaching of rheology to undergraduates and graduate students working in chemical and biomolecular engineering, chemistry, physics and materials science at Rice University.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.