Flying insects have evolved sophisticated sensory–motor systems, and here we argue that such systems are used to keep upright against intrinsic flight instabilities. We describe a theory that predicts the instability growth rate in body pitch from flapping-wing aerodynamics and reveals two ways of achieving balanced flight: active control with sufficiently rapid reactions and passive stabilization with high body drag. By glueing magnets to fruit flies and perturbing their flight using magnetic impulses, we show that these insects employ active control that is indeed fast relative to the instability. Moreover, we find that fruit flies with their control sensors disabled can keep upright if high-drag fibres are also attached to their bodies, an observation consistent with our prediction for the passive stability condition. Finally, we extend this framework to unify the control strategies used by hovering animals and also furnish criteria for achieving pitch stability in flapping-wing robots.

Gelation of aqueous methylcellulose (MC) solutions upon heating has been shown to result from the formation of a network of semiflexible fibrils, with diameters of 15 ± 2 nm. Here, we investigate the impact of MC molecular weight on the elasticity and structure of aqueous gels at concentrations between 0.1 and 3 wt %. Small-amplitude oscillatory shear measurements conducted at a fixed concentration reveal that the gel modulus increases monotonically by a factor of 5 for weight-average molecular weights (M w ) between 22 and 550 kg/mol. Small-angle X-ray scattering data, fit to a semiflexible cylinder model, demonstrate that the fibril radius, Kuhn length, and volume fraction are approximately constant throughout this molecular weight range. Small-angle light scattering shows that the fibrillar-rich and fibrillar-depleted domains within the gel are associated with an essentially invariant heterogeneity correlation length. Direct visualization by cryo-TEM reveals that lower molecular weight MC forms fibrils of lower average length. The distribution of fibril lengths measured by cryo-TEM and the distribution of the polymer chain contour lengths are similar, especially for shorter chains, and these features are correlated to network connectivity. We propose that the underlying fibril structure consists of bundles of polymer chains with a preferred orientation coincident with the fibril axis, while the fibril diameter is controlled by a circumferential helical pitch associated with the single chain Kuhn length and interactions between chains.

We have studied the influence of segmental dipole orientation on the solution properties of polyzwitterions using dynamic and static light scattering of poly(2methacryloyloxyethyl phosphorylcholine) (PMPC), n-butylsubstituted choline phosphate polymers (PMBP), and their diblock (PMPC-b-PMBP) copolymers in solutions of different salt concentration. We find that these three structures exhibit dramatically different aggregation behaviors. For the conditions in our study, PMPC is a swollen excluded-volume chain without significant presence of dipolar correlations as evident from the lack of sensitivity to the ionic strength of the solution. In contrast, PMBP self-assembles into finite-sized structures in solution, which are stabilized by electrostatic dipole−dipole interactions. Evidence of these interactions is also present in the diblock polymer, PMPB-b-PMPC, which self-assembles into two distinct, stable aggregates in addition to unaggregated chains. These results contribute to the breadth of understanding of polyzwitterions in solution and provide a platform for future simulation and experimental explorations.

Low molecular weight thiol-terminated poly-(ethylene glycol) (PEG) (M ≈ 800) has been grafted onto a high molecular weight methylcellulose (MC, M w ≈ 150000) by a facile thiol−ene click reaction; graft densities varied from 0.7% to 33% (grafts per anhydroglucose unit). Static and dynamic light scattering reveals that the overall radius of the chain increases systematically with graft density, in a manner in excellent agreement with theory. As the contour length remains unchanged, it is apparent that grafting leads to an increase in the persistence length of this semiflexible copolymer, by as much as a factor of 4. These results represent the first experimental verification of the excluded volume theory at low grafting densities, and demonstrate a promising synthetic platform for systematically increasing the persistence length of a model semiflexible, water-soluble polymer.

We investigate the effect of short-chain poly­(ethylene glycol) (PEG) graft density on the formation of methylcellulose (MC) fibrils at elevated temperatures. Thiol–ene click chemistry was used to systematically graft 800 and 2000 g/mol PEG onto the backbone of allylated MC, with a wide range of grafting densities from 0.7% to 33%. As determined from light scattering, grafting leads to an increase in the persistence length of this semiflexible copolymer, by as much as a factor of 10. Upon heating, SAXS and AFM studies show that fibril formation is suppressed at around 10% grafting density for shorter PEG grafts, corresponding to persistence lengths about ∼22 nm. For longer grafts fibril formation is suppressed at 7% grafting density, at around the same ∼22 nm persistence length. The radius of the fibrils increases with the square root of the persistence length of the chains, which is consistent with a theory for the radius of twisted chains. The ability to form networks at 80 °C is highly correlated to the ability to form fibrils, and accordingly the modulus systematically decreases with grafting density. When the fibril formation is suppressed, MC solutions no longer form solid networks. Therefore, grafting modulates the molecular architecture and gelation properties of MC and also provides new insight into the structure of MC fibrils.

Methylcellulose (MC) is a water-soluble cellulose derivative with a wide range of commercial applications. Upon heating, MC solutions reversibly form ∼15–20 nm diameter fibrils, which percolate into a fibrillar network, resulting in macroscopic gelation. Using mid-angle X-ray scattering (MAXS) and wide-angle X-ray scattering (WAXS), we have analyzed MC chain organization within fibrils aligned in dried films that have been stretched by over 300%. MAXS and WAXS show distinct anisotropic scattering features, which we interpret as reflecting crystalline domains within the fibrils. The scattering peaks are consistent with a body-centered monoclinic unit cell, with similar dimensions as other cellulosic crystals, a = 11.4 Å, b = 8.9 Å, and c = 10.2 Å, and γ in the range of 90–100°, with MC chains oriented along the long axis of the fibril. Phase-plate cryogenic transmission electron microscopy images of MC fibrils contribute to a more comprehensive picture. Along the long axis of MC fibrils, there is evidence of dense twisted domains, which are interpreted as regions containing semicrystalline MC, interspersed with looser, less organized amorphous domains. Together, these two techniques provide the most complete interpretation of MC subfibril structure currently available.

When a water drop is placed onto a soft polymer network, a wetting ridge develops at the drop periphery. The height of this wetting ridge is typically governed by the drop surface tension balanced by elastic restoring forces of the polymer network. However, the situation is more complex when the network is swollen with fluid, because the fluid may separate from the network at the contact line. Here we study the fluid separation and network deformation at the contact line of a soft polydimethylsiloxane (PDMS) network, swollen with silicone oil. By controlling both the degrees of crosslinking and swelling, we find that more fluid separates from the network with increasing swelling. Above a certain swelling, network deformation decreases while fluid separation increases, demonstrating synergy between network deformation and fluid separation. When the PDMS network is swollen with a fluid having a negative spreading parameter, such as hexadecane, no fluid separation is observed. A simple balance of interfacial, elastic, and mixing energies can describe this fluid separation behavior. Our results reveal that a swelling fluid, commonly found in soft networks, plays a critical role in a wetting ridge.

The thermoresponsive behavior of a hydroxypropylmethylcellulose (HPMC) sample in aqueous solutions has been studied by a powerful combination of characterization tools, including rheology, turbidimetry, cryogenic transmission electron microscopy (cryoTEM), light scattering, small-angle neutron scattering (SANS), and small-angle X-ray scattering (SAXS). Consistent with prior literature, solutions with concentrations ranging from 0.3 to 3 wt % exhibit a sharp drop in the dynamic viscoelastic moduli G' and G″ upon heating near 57 °C. The drop in moduli is accompanied by an abrupt increase in turbidity. All the evidence is consistent with this corresponding to liquid-liquid phase separation, leading to polymer-rich droplets in a polymer-depleted matrix. Upon further heating, the moduli increase, and G' exceeds G″, corresponding to gelation. CryoTEM in dilute solutions reveals that HPMC forms fibrils at the same temperature range where the moduli increase. SANS and SAXS confirm the appearance of fibrils over a range of concentration, and that their average diameter is ca. 18 nm; thus gelation is attributable to formation of a sample-spanning network of fibrils. These results are compared in detail with the closely related and well-studied methylcellulose (MC). The HPMC fibrils are generally shorter, more flexible, and contain more water than with MC, and the resulting gel at high temperatures has a much lower modulus. In addition to the differences in fibril structure, the key distinction between HPMC and MC is that the former undergoes liquid-liquid phase separation prior to forming fibrils and associated gelation, whereas the latter forms fibrils first. These results and their interpretation are compared with the prior literature, in light of the relatively recent discovery of the propensity of MC and HPMC to self-assemble into fibrils on heating.