Polydispersity helps encode soft material network structures

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Jan 10, 2020

Image credit: Wei-Shao Wei, Arjun G. Yodh, and Felice Macera
This post was written by Wei-Shao Wei, Prof. Arjun G. Yodh, Prof. Shu Yang, Sophie Ettinger, and Yu Xia

Homogeneous samples, or samples with monodisperse ingredients, are usually desirable for materials applications. Experimentally, polydispersity or molecular heterogeneity tends to introduce disorder into materials, which often (but not always!) impedes self-assembly and phase-transitions. Theoretically, monodisperse systems are easier to model and understand, and they offer unified starting points for exploration of “non-ideal” matter.

Nevertheless, in the world around us, most materials are intrinsically heterogeneous or polydisperse. Natural polymers like rubber, wood cellulose, and silk are composed of long-chain molecules with many different lengths. Natural and practical dispersions - solid particles in liquids, liquid drops in liquids or in gasses, etc. - are comprised of constituents with a wide distribution of sizes. Moreover, in biological matter, molecular heterogeneity can help promote formation of diverse surface patterns and morphologies in pollen grains, insect cuticles, fungal spores, as well as the photonic structures in butterfly wings and bird feathers.

The findings we recently published in Nature reported on dramatic shape transformations of liquid crystal (LC) drops. Interestingly, we found that these changes in morphology were driven by the polydispersity of the molecules contained inside the drop.

This research was fun, in large part because of the beautiful shape-transformation effects, but also because the explanation we needed to understand this phenomenon was a complete surprise. We first tackled the problem with traditional reasoning, modeling the drop and its contents as a monodisperse material. To our surprise, this approach failed dramatically and forced us to confront the influence of polydispersity. A new mechanistic feature due to polydispersity showed how molecular polydispersity, surface tension, and bulk elastic energy could conspire to promote morphological change. For the modeling, it helped that our drops were equilibrium systems. However, the central ideas we uncovered about the effects of molecular segregation of polydisperse matter should apply broadly to living, non-equilibrium, and thermal matter. 

To appreciate the shape-changing effects, first check out an eye-catching video (above) that summarizes our story. Briefly, we started with drops composed of polydisperse nematic liquid crystal oligomers (NLCOs) in a solution of water and surfactants. Oligomers are low molecular weight polymers consisting of a few repeating units. The liquid crystal oligomers, in this case, are rod-like molecules that impart anisotropic properties to the soft material due to alignment of the rods. The rods are translationally disordered but are orientationally ordered. (These anisotropic properties and accompanying responses are crucial for LC display technologies!) When we vary the temperature, the drops change shape. Lowering the temperature causes spherical drops (left side, panel below) to evolve into filamentous drops (right side, panel below). Moreover, these polymorphic shape transitions are reversible and repeatable via temperature cycling.

We thought we could understand this effect as a simple competition between surface tension (i.e., associated with the interface between the different fluids inside and outside of the drop) and bulk free energy of the LC inside the drop. Using measurements of drop diameter (for sphere) and cylinder radius (for filaments), surface tension, and estimates for the NLCO elastic energy based on well-understood models of monodisperse LCs, we computed conditions for which such shape transitions should occur. Surprisingly, the calculations did not agree with experiment and required truly unphysical elastic constants for the LCs. This dramatic disagreement between theory and experiment forced us to consider the effects of polydispersity.

In practice, even though we modeled them as such, the NLCOs in the drop are not monodisperse. Rather, each surfactant-stabilized NLCO emulsion drop contained a mixture of monomers and oligomers with a wide range of chain lengths. In the figure below, we illustrate the situation. For simplicity, we approximate the continuous distribution of oligomers with just two types of oligomers in the drop: long-chain and short-chain. We illustrate the key new effect in the figure; it arises because the elastic forces vary with position in the drops and because the polydisperse oligomers can migrate in response to these forces. Elastic energy gradients of the LC director (LC alignment field) cause the long-chain oligomers to move away from the drop center towards the drop surface. This micro-segregation effect lowers the bulk free energy of the drop (more for the cylindrical than spherical drop) and it substantially lowers the surface tension by enhancing local alignment on the drop surface. Thus, spatial redistribution of polydisperse oligomers leads to the observed sphere-filament shape instability.


As a result of molecular polydispersity, the drops self-assembled into a stunning array of complex nematic LC structures, ranging from “flowers” to massive “Medusa” networks of intertwining fibers (see video clip). In previous research, we have encountered and been captivated by counterintuitive “order from disorder” self-assembly effects and forces. Nevertheless, the present experiments were extraordinary because a different phenomenon was revealed to us, wherein disorder, in this case polydispersity, provided means to create new network structures from soft materials. 

Finally, for the future, it is interesting to “crosslink” the NLCOs using UV light into so-called nematic liquid crystal elastomers (NLCEs). This was our motivation at the outset. We show some of these “frozen” structures in electron microscopy images (above). This NLCE capability opens possibilities for creation of responsive soft matter network structures, and we are currently carrying out new experiments along these lines. Looking back though, perhaps the most exciting finding of our work was the surprising role of polydispersity in driving these phenomena. We hope other researchers will feel encouraged to explore the potential influences of molecular heterogeneity in both living and non-living matter. (For more information at the general-reader level, see Penn Today Newsletters.)

Go to the profile of Wei-Shao Wei

Wei-Shao Wei

PhD candidate, University of Pennsylvania

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