Traveling Perversion as Constant Torque Actuator.

Mechanical stress and conformation of helical elastic rods clamped at both ends were studied upon unwinding. By axial rotation of one end, the winding number was progressively changed from the natural one (n=n_{0}) to complete chirality inversion (n=-n_{0}) while keeping the total elongation fixed and monitoring the applied torque M and tension T. Along the unwinding process, the system crosses three distinct states: natural helix (+), mixed state (+/-), and inverted helix (-). The mixed state involves two helices with opposite chiralities spatially connected by a perversion (helicity inversion). Upon unwinding, the perversion is "injected" (nucleated) from one side and travels toward the opposite side where it is eventually "absorbed" (annihilated), leaving the system in the (-) state. In the mixed state, the profile of M(n) is almost flat: the system behaves as a constant torque actuator. The three states are quantitatively well described in the framework of a biphasic model which neglects the perversion energy and finite size effects. The latter are taken into account in a numerical simulation based on the Kirchhoff theory of elastic rods. The traveling perversion in helical elastic rods and related topological phenomena are universal, with applications from condensed matter to biological and bioinspired systems, including in particular mechanical engineering and soft robotics.

Extraction of Silicone Uncrosslinked Chains at Air-Water-Polydimethylsiloxane Triple Lines.

Silicone elastomers such as polydimethylsiloxane (PDMS) are convenient materials routinely used in laboratories that combine ease of preparation, flexibility, transparency, and gas permeability. However, these elastomers are known to contain a small fraction of uncrosslinked low-molecular-weight oligomers, the effects of which are not completely understood, particularly when used in contact with liquids. Here, we show that triple lines involving air, water, and PDMS elastomers are responsible for the contamination of water-air interfaces by uncrosslinked silicone oligomers through a capillarity-induced extraction mechanism. We investigate both the case of static and moving contact lines and study various geometries ranging from partially immersed PDMS plates to water droplets or air bubbles deposited on PDMS plates, all involving air-water-elastomer triple lines. We demonstrate experimentally that the contamination timescale is strikingly shorter for moving contact lines than in the static case. Eventually, we propose a simple poroelastic model capturing the main features of contamination observed in experiments.

Capillarity-induced folds fuel extreme shape changes in thin wicked membranes.

Soft deformable materials are needed for applications such as stretchable electronics, smart textiles, or soft biomedical devices. However, the design of a durable, cost-effective, or biologically compatible version of such a material remains challenging. Living animal cells routinely cope with extreme deformations by unfolding preformed membrane reservoirs available in the form of microvilli or membrane folds. We synthetically mimicked this behavior by creating nanofibrous liquid-infused tissues that spontaneously form similar reservoirs through capillarity-induced folding. By understanding the physics of membrane buckling within the liquid film, we developed proof-of-concept conformable chemical surface treatments and stretchable basic electronic circuits.

Auxiliary soft beam for the amplification of the elasto-capillary coiling: Towards stretchable electronics.

A flexible fiber carrying a liquid drop may coil inside the drop thereby creating a drop-on-fiber system with an ultra-extensible behavior. During compression, the excess fiber is spooled inside the droplet and capillary forces keep the system taut. During subsequent elongation, the fiber is gradually released and if a large number of spools is uncoiled a high stretchability is achieved. This mechanical behaviour is of interest for stretchable connectors but information, may it be electronic or photonic, usually travels through stiff functional materials. These high Young's moduli, leading to large bending rigidity, prevent in-drop coiling. Here we overcome this limitation by attaching a beam of soft elastomer to the functional fiber, thereby creating a composite system which exhibits in-drop coiling and carries information while being ultra-extensible. We present a simple model to explain the underlying mechanics of the addition of the soft beam and we show how it favors in-drop coiling. We illustrate the method with a two-centimeter long micronic PEDOT:PSS conductive fiber joined to a PVS soft beam, showing that the system conveys electricity throughout a 1900% elongation.

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology.

We investigate the mechanics of elastic fibres carrying liquid droplets. In such systems, buckling may localize inside the drop cavity if the fibre is thin enough. This so-called drop-on-coilable-fibre system exhibits a surprising liquid-like response under compression and a solid-like response under tension. Here we analyze this unconventional behavior in further detail and find theoretical, numerical and experimental evidence of negative stiffness events. We find that the first and main negative stiffness regime owes its existence to the transfer of capillary-stored energy into mechanical curvature energy. The following negative stiffness events are associated with changes in the coiling morphology of the fibre. Eventually coiling becomes tightly locked into an ordered phase where liquid and solid deformations coexist.

Role of uncrosslinked chains in droplets dynamics on silicone elastomers.

We report an unexpected behavior in wetting dynamics on soft silicone substrates: the dynamics of aqueous droplets deposited on vertical plates of such elastomers exhibits two successive speed regimes. This macroscopic observation is found to be closely related to microscopic phenomena occurring at the scale of the polymer network: we show that uncrosslinked chains found in most widely used commercial silicone elastomers are responsible for this surprising behavior. A direct visualization of the uncrosslinked oligomers collected by water droplets is performed, evidencing that a capillarity-induced phase separation occurs: uncrosslinked oligomers are extracted from the silicone elastomer network by the water-glycerol mixture droplet. The sharp speed change is shown to coincide with an abrupt transition in surface tension of the droplets, when a critical surface concentration in uncrosslinked oligomer chains is reached. We infer that a droplet shifts to a second regime with a faster speed when it is completely covered with a homogeneous oil film.

In-drop capillary spooling of spider capture thread inspires hybrid fibers with mixed solid-liquid mechanical properties.

An essential element in the web-trap architecture, the capture silk spun by ecribellate orb spiders consists of glue droplets sitting astride a silk filament. Mechanically this thread presents a mixed solid-liquid behavior unknown to date. Under extension, capture silk behaves as a particularly stretchy solid, owing to its molecular nanosprings, but it totally switches behavior in compression to now become liquid-like: It shrinks with no apparent limit while exerting a constant tension. Here, we unravel the physics underpinning the unique behavior of this "liquid wire" and demonstrate that its mechanical response originates in the shape-switching of the silk filament induced by buckling within the droplets. Learning from this natural example of geometry and mechanics, we manufactured programmable liquid wires that present previously unidentified pathways for the design of new hybrid solid-liquid materials.

Adhesion of dry and wet electrostatic capture silk of uloborid spider.

We demonstrate the impressive adhesive qualities of uloborid spider orb-web capture when dry, which are lost when the nano-filament threads are wetted. A force sensor with a 50 nN-1 mN detection sensitively allowed us to measure quantitatively the stress-strain characteristics of native silk threads in both the original dry state and after wetting by controlled application of water mist with droplet sizes ranging between 3 and 5 µm and densities ranging between 10(4) and 10(5) per mm(3). Stress forces of between 1 and 5 µN/µm(2) in the native, dry multifilament thread puffs were reduced to between 0.1 and 0.5 µN/µm(2) in the wetted collapsed state, with strain displacements reducing from between 2 and 5 mm in the dry to 0.10-0.12 mm in the wetted states. We conclude that wetting cribellate threads reduce their van der Waals adhesion with implications on the thread's adhesive strength under tension. This should be considered when discussing the evolutionary transitions of capture silks from the ancestral dry-state nano-filaments of the cribellate spider taxa to the wet-state glue-droplets of the ecribellate taxa.

Elastocapillary snapping: capillarity induces snap-through instabilities in small elastic beams.

We report on the capillarity-induced snapping of elastic beams. We show that a millimeter-sized water drop gently deposited on a thin buckled polymer strip may trigger an elastocapillary snap-through instability. We investigate experimentally and theoretically the statics and dynamics of this phenomenon and we further demonstrate that snapping can act against gravity, or be induced by soap bubbles on centimeter-sized thin metal strips. We argue that this phenomenon is suitable to miniaturization and design a condensation-induced spin-off version of the experiment involving a hydrophilic strip placed in a steam flow.

Global force-torque phase diagram for the DNA double helix: structural transitions, triple points, and collapsed plectonemes.

We present a free energy model for structural transitions of the DNA double helix driven by tensile and torsional stress. Our model is coarse grained and is based on semiflexible polymer descriptions of B-DNA, underwound L-DNA, and highly overwound P-DNA. The statistical-mechanical model of plectonemic supercoiling previously developed for B-DNA is applied to semiflexible polymer models of P- and L-DNA to obtain a model of DNA structural transitions in quantitative accord with experiment. We identify two distinct plectonemic states, one "inflated" by electrostatic repulsion and thermal fluctuations and the other "collapsed," with the two double helices inside the supercoils driven to close contact. We find that supercoiled B and L are stable only in the inflated form, while supercoiled P is always collapsed. We also predict the behavior and experimental signatures of highly underwound "Q"-DNA, the left-handed analog of P-DNA; as for P, supercoiled Q is always collapsed. Overstretched "S"-DNA and strand-separated "stress-melted" DNA are also included in our model, allowing prediction of a global phase diagram for forces up to 1000 pN and torques between ±60 pN nm, or, in terms of linking number density, from σ=-5 to +3.

Competition between curls and plectonemes near the buckling transition of stretched supercoiled DNA.

Recent single-molecule experiments have observed that formation of a plectonemically supercoiled region in a stretched, twisted DNA proceeds via abrupt formation of a small plectonemic "bubble." A detailed mesoscopic model is presented for the formation of plectonemic domains, including their positional entropy, and the influence of small chiral loops or "curls" along the extended DNA. Curls begin to appear just before plectoneme formation, and are more numerous at low salt concentrations (<20 mM univalent ions) and at low forces (<0.5 pN). However, plectonemic domains quickly become far more stable slightly beyond the transition to supercoiling at moderate forces and physiological salt conditions. At the supercoiling transition, for shorter DNAs (2 kb) only one supercoiled domain appears, but for longer DNAs at lower forces (<0.5 pN) positional entropy favors formation of more than one plectonemic domain; a similar effect occurs for low salt. Although they are not the prevalent mode of supercoiling, curls are a natural transition state for binding of DNA-loop-trapping enzymes; we show how addition of loop-trapping enzymes can modify the supercoiling transition. The behavior of DNA torque is also discussed, including the effect of the measurement apparatus torque stiffness, which can play a role in determining how large the torque "overshoot" is at the buckling transition.

Instant fabrication and selection of folded structures using drop impact.

A drop impacting a target cutout in a thin polymer film is wrapped by the film in a dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from a given target by slightly varying the impact parameters. A simplified model for a nonlinear dynamic Elastica coupled with a drop successfully explains this shape selection and yields detailed quantitative agreement with experiments. This first venture into the largely unexplored dynamics of elastocapillary assemblies opens up the perspective of mass production of 3D packages with individual shape selection.

Analytical description of extension, torque, and supercoiling radius of a stretched twisted DNA.

We study the mixture of extended and supercoiled DNA that occurs in a twisted DNA molecule under tension. Closed-form asymptotic solutions for the supercoiling radius, extension, and torque of the molecule are obtained in the high-force limit where electrostatic and elastic effects dominate. We demonstrate that experimental data obey the extension and torque scaling laws apparent in our formulas, in the regime where thermal fluctuation effects are quenched by applied force.

Friction of F-actin knots.

We use the existing data of force-extension experiments on F-actin molecules tied into knots to compute a value of 0.15 for the static friction coefficient for contact between different parts of the same molecule with itself. This estimate for protein-protein friction is relevant for the stabilization of the 273 known proteins with knots, one percent of the structures deposited in the Protein Data Bank.

Polyhelices through n points.

A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial position, the signed curvature, torsion, and length of each helical segment. Polyhelices can be parametrised by the arc length and easily expressed in terms of product of matrices.

Writhe formulas and antipodal points in plectonemic DNA configurations.

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double helix, these numbers are not always straightforward to compute, though a simplified formula was established in a theorem by Fuller [Proc. Natl. Acad. Sci. U.S.A. 75, 3557 (1978)]. We examine the range of applicability of this widely used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.

Chirality of coiled coils: elasticity matters.

Coiled coils are important protein-protein interaction motifs with high specificity that are used to assemble macromolecular complexes. Their simple geometric organization, consisting of alpha helices wrapped around each other, confers remarkable mechanical properties. A geometrical and mechanical continuous model taking into account sequence effects and based on the superhelical winding of the constituent helices is introduced, and a continuous family of solutions in which the oligomerization interactions are satisfied is derived. From these solutions, geometric and structural properties, such as the chirality and pitch of the coiled coil and the location of residues, are obtained. The theoretical predictions are compared to x-ray data from the leucine zipper motif.

Mechanics of climbing and attachment in twining plants.

Twining plants achieve vertical growth by revolving around supports of different sizes on which they exert a pressure. This observation raises many intriguing questions that are addressed within the framework of elastic filamentary structures by modeling the stem close to the apex as a growing elastic rod. The analysis shows that vertical growth is achieved thanks to discrete contact points and regions with continuous contact, that the contact pressure creates tension in the stem as observed experimentally, and that there is a maximal radius of the pole around which a twiner can climb.

Fragmentation of rods by cascading cracks: why spaghetti does not break in half.

When thin brittle rods such as dry spaghetti pasta are bent beyond their limit curvature, they often break into more than two pieces, typically three or four. With the aim of understanding these multiple breakings, we study the dynamics of a bent rod that is suddenly released at one end. We find that the sudden relaxation of the curvature at this end leads to a burst of flexural waves, whose dynamics are described by a self-similar solution with no adjustable parameters. These flexural waves locally increase the curvature in the rod, and we argue that this counterintuitive mechanism is responsible for the fragmentation of brittle rods under bending. A simple experiment supporting the claim is presented.

Extracting DNA twist rigidity from experimental supercoiling data.

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we obtain an estimate of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immersed.