A Topologically Driven Glass in Ring Polymers (1510.05625v3)

Abstract: The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in Polymer Physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly inter-penetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work demonstrates both the existence of long-lived inter-ring penetrations and also realises a novel, topologically-induced, glass transition.

• The paper demonstrates that topological threadings induce a kinetic arrest, creating a glassy state in ring polymers distinct from classical transitions in linear polymers.
• Using selective pinning experiments, the study quantitatively shows how immobilizing a fraction of rings significantly hinders the diffusion of unpinned rings.
• The findings indicate that the glass transition is exponentially sensitive to polymer length, offering new insights for designing advanced materials in complex fluids.

Analyzing "A Topologically Driven Glass in Ring Polymers"

The paper "A Topologically Driven Glass in Ring Polymers" by Davide Michieletto and Matthew S. Turner investigates the glass transition phenomena in systems of ring polymers. The paper's focal point is a concentrated solution of ring polymers, with a particular emphasis on understanding how topological constraints influence their dynamic behavior. Notably, the authors propose that a kinetic arrest of rings can be driven by topological interactions, termed "threadings," which signify a profound departure from the behavior of linear polymers.

Key Findings

1. Topological Interactions and Glass Transition: The paper demonstrates a novel glass transition in ring polymers precipitated by threadings - complex inter-penetrations of rings. These interactions create a kinetic arrest state that significantly diverges from the classical glass transition mechanisms observed in linear polymers, which are predominantly temperature or density driven.
2. Experimental Approach and Evidence: The authors introduce a new method to explore this transition. By selectively "pinning" a fraction of the rings, they observe the resulting behavior of the remaining unpinned rings. This intervention provides compelling evidence of the threadings as it quantitatively illustrates how a small fraction of pinned rings can immobilize the unpinned rings.
3. Implications on Diffusion and Dynamics: Ring polymers, due to their closed-loop nature, lack free ends, restricting their diffusive capabilities compared to their linear counterparts. The paper shows that these topological constraints increase the timescale of dynamic correlations, suggesting a slow, heterogeneous dynamic akin to glassy behavior as the length of the ring polymers increases.
4. Kinetically Arrested States: Remarkably, it is shown that ring polymers can exhibit a form of glassy kinetic arrest even at temperatures above the classical glass transition temperature. This arrest does not only arise from threading, but also appears sensitive to polymer length, becoming exponentially more pronounced with longer chains.

Numerical Results

Several numerical simulations underpin these findings, detailing the relationship between chain length, the fraction of pinned rings, and the transition to a glassy state. Importantly, the work predicts that as ring polymers become sufficiently long, this novel jamming transition occurs with an infinitesimal fraction of pinned chains, illustrating an exponential sensitivity to their length.

Theoretical and Practical Implications

Theoretically, this work introduces a unique perspective on glass transitions, suggesting that topology itself can drive such states in polymer systems. This contributes to the broader understanding of the dynamics in polymer physics and complex fluids, especially in systems where classical explanations cannot fully describe observed phenomena.

Practically, these findings pave the way for novel materials design. The unique behaviors of ring polymers could be harnessed in applications where durable, high-viscosity, or permanently stable states are advantageous. Moreover, the results could have implications in biological systems where ring-like structures play crucial roles, such as chromosome organization within cells.

Future Developments

Future research could extend this work to explore the effects of other topological constraints, such as knotted rings, and their impact on dynamics. Additionally, investigating how external fields or complex environmental conditions (e.g., varying solvent quality or confinement) interact with these topological glass states could further advance the field. Such studies could delve even further into the intricate balance of enthalpic and entropic factors that define the kinetic and thermodynamic landscape of these fascinating systems.

In summary, Michieletto and Turner's research offers a comprehensive and innovative exploration of the glassy behaviors in ring polymers arising from topological effects. Their work contributes significantly to both the theoretical framework and the potential practical utilization of ring polymers in advanced material science and biotechnology.