Bottlebrush Networks: A Primer for Advanced Architectures.

Bottlebrush networks (BBNs) are an exciting new class of materials with interesting physical properties derived from their unique architecture. While great strides have been made in our fundamental understanding of bottlebrush polymers and networks, an interdisciplinary approach is necessary for the field to accelerate advancements. This review aims to act as a primer to BBN chemistry and physics for both new and current members of the community. In addition to providing an overview of contemporary BBN synthetic methods, we developed a workflow and desktop application (LengthScale), enabling bottlebrush physics to be more approachable. We conclude by addressing several topical issues and asking a series of pointed questions to stimulate conversation within the community.

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.

Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems.

A Tunable, Simplified Model for Biological Latch Mediated Spring Actuated Systems.

We develop a model of latch-mediated spring actuated (LaMSA) systems relevant to comparative biomechanics and bioinspired design. The model contains five components: two motors (muscles), a spring, a latch, and a load mass. One motor loads the spring to store elastic energy and the second motor subsequently removes the latch, which releases the spring and causes movement of the load mass. We develop freely available software to accompany the model, which provides an extensible framework for simulating LaMSA systems. Output from the simulation includes information from the loading and release phases of motion, which can be used to calculate kinematic performance metrics that are important for biomechanical function. In parallel, we simulate a comparable, directly actuated system that uses the same motor and mass combinations as the LaMSA simulations. By rapidly iterating through biologically relevant input parameters to the model, simulated kinematic performance differences between LaMSA and directly actuated systems can be used to explore the evolutionary dynamics of biological LaMSA systems and uncover design principles for bioinspired LaMSA systems. As proof of principle of this concept, we compare a LaMSA simulation to a directly actuated simulation that includes either a Hill-type force-velocity trade-off or muscle activation dynamics, or both. For the biologically-relevant range of parameters explored, we find that the muscle force-velocity trade-off and muscle activation have similar effects on directly actuated performance. Including both of these dynamic muscle properties increases the accelerated mass range where a LaMSA system outperforms a directly actuated one.

The Impact of Polymerization Chemistry on the Mechanical Properties of Poly(dimethylsiloxane) Bottlebrush Elastomers.

We compare the low-strain mechanical properties of bottlebrush elastomers (BBEs) synthesized using ring-opening metathesis and free radical polymerization. Through comparison of experimentally measured elastic moduli and those predicted by an ideal, affine model, we evaluate the efficiency of our networks in forming stress-supporting strands. This comparison allowed us to develop a structural efficiency ratio that facilitates the prediction of mechanical properties relative to polymerization chemistry (e.g., softer BBEs when polymerizing under dilute conditions). This work highlights the impact that polymerization chemistry has on the structural efficiency ratio and the resultant mechanical properties of BBEs with identical side chains, providing another "knob" by which to control polymer network properties.

The ultrafast snap of a finger is mediated by skin friction.

The snap of a finger has been used as a form of communication and music for millennia across human cultures. However, a systematic analysis of the dynamics of this rapid motion has not yet been performed. Using high-speed imaging and force sensors, we analyse the dynamics of the finger snap. We discover that the finger snap achieves peak angular accelerations of 1.6 × 106° s-2 in 7 ms, making it one of the fastest recorded angular accelerations the human body produces (exceeding professional baseball pitches). Our analysis reveals the central role of skin friction in mediating the snap dynamics by acting as a latch to control the resulting high velocities and accelerations. We evaluate the role of this frictional latch experimentally, by covering the thumb and middle finger with different materials to produce different friction coefficients and varying compressibility. In doing so, we reveal that the compressible, frictional latch of the finger pads likely operates in a regime optimally tuned for both friction and compression. We also develop a soft, compressible friction-based latch-mediated spring actuated model to further elucidate the key role of friction and how it interacts with a compressible latch. Our mathematical model reveals that friction plays a dual role in the finger snap, both aiding in force loading and energy storage while hindering energy release. Our work reveals how friction between surfaces can be harnessed as a tunable latch system and provides design insight towards the frictional complexity in many robotic and ultra-fast energy-release structures.

Latch-based control of energy output in spring actuated systems.

The inherent force-velocity trade-off of muscles and motors can be overcome by instead loading and releasing energy in springs to power extreme movements. A key component of this paradigm is the latch that mediates the release of spring energy to power the motion. Latches have traditionally been considered as switches; they maintain spring compression in one state and allow the spring to release energy without constraint in the other. Using a mathematical model of a simplified contact latch, we reproduce this instantaneous release behaviour and also demonstrate that changing latch parameters (latch release velocity and radius) can reduce and delay the energy released by the spring. We identify a critical threshold between instantaneous and delayed release that depends on the latch, spring, and mass of the system. Systems with stiff springs and small mass can attain a wide range of output performance, including instantaneous behaviour, by changing latch release velocity. We validate this model in both a physical experiment as well as with data from the Dracula ant, Mystrium camillae, and propose that latch release velocity can be used in both engineering and biological systems to control energy output.

The effect of size-scale on the kinematics of elastic energy release.

Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands that efficiently cycle mechanical energy with minimal loss. The maximum center-of-mass velocity of the elastomer bands was found to be size-scale independent, while smaller bands demonstrated larger accelerations and shorter durations of elastic energy release. Scaling relationships determined from these measurements are consistent with the performance of small organisms and engineered devices which utilize elastic elements to power motion.

Why do Large Animals Never Actuate Their Jumps with Latch-Mediated Springs? Because They can Jump Higher Without Them.

As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable work in even larger animals, why don't larger animals use spring-actuated jumping systems as well? We will show that muscle length-tension properties limit spring-actuated systems to generating a maximum one-third of the possible work that a muscle could produce-greatly restricting the jumping height of spring-actuated jumpers. Thus a spring-actuated jumping animal has a jumping height that is one-third of the maximum possible jump height achievable were 100% of the possible muscle work available. Larger animals, which could theoretically use all of the available muscle energy, have a maximum jumping height that asymptotically approaches a value that is about three times higher than that of spring-actuated jumpers. Furthermore, a size related "crossover point" is evident for these two jumping mechanisms: animals smaller than this point can jump higher with a spring-actuated mechanism, while animals larger than this point can jump higher with a muscle-actuated mechanism. We demonstrate how this limit on energy storage is a consequence of the interaction between length-tension properties of muscles and spring stiffness. We indicate where this crossover point occurs based on modeling and then use jumping data from the literature to validate that larger jumping animals generate greater jump heights with muscle-actuated systems than spring-actuated systems.

The principles of cascading power limits in small, fast biological and engineered systems.

Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Adsorption-induced slip inhibition for polymer melts on ideal substrates.

Hydrodynamic slip, the motion of a liquid along a solid surface, represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with polymer reptation implies extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de Gennes model was confirmed using dewetting experiments on ultra-smooth, low-energy substrates. Here, we use capillary leveling-surface tension driven flow of films with initially non-uniform thickness-of polymeric films on these same substrates. Measurement of the slip length from a robust one parameter fit to a lubrication model is achieved. We show that at the low shear rates involved in leveling experiments as compared to dewetting ones, the employed substrates can no longer be considered ideal. The data is instead consistent with a model that includes physical adsorption of polymer chains at the solid/liquid interface.

Direct Measurement of the Critical Pore Size in a Model Membrane.

We study pore nucleation in a model membrane system, a freestanding polymer film. Nucleated pores smaller than a critical size close, while pores larger than the critical size grow. Holes of varying size were purposefully prepared in liquid polymer films, and their evolution in time was monitored using optical and atomic force microscopy to extract a critical radius. The critical radius scales linearly with film thickness for a homopolymer film. The results agree with a simple model which takes into account the energy cost due to surface area at the edge of the pore. The energy cost at the edge of the pore is experimentally varied by using a lamellar-forming diblock copolymer membrane. The underlying molecular architecture causes increased frustration at the pore edge resulting in an enhanced cost of pore formation.

Capillary Leveling of Freestanding Liquid Nanofilms.

We report on the capillary-driven leveling of a topographical perturbation at the surface of a freestanding liquid nanofilm. The width of a stepped surface profile is found to evolve as the square root of time. The hydrodynamic model is in excellent agreement with the experimental data. In addition to exhibiting an analogy with diffusive processes, this novel system serves as a precise nanoprobe for the rheology of liquids at interfaces in a configuration that avoids substrate effects.

Onset of Area-Dependent Dissipation in Droplet Spreading.

We probe the viscous relaxation of structured liquid droplets in the partial wetting regime using a diblock copolymer system. The relaxation time of the droplets is measured after a step change in temperature as a function of three tunable parameters: droplet size, equilibrium contact angle, and the viscosity of the fluid. Contrary to what is typically observed, the late-stage relaxation time does not scale with the radius of the droplet-rather, relaxation scales with the radius squared. Thus, the energy dissipation depends on the contact area of the droplet, rather than the contact line.

Quantized contact angles in the dewetting of a structured liquid.

We investigate the dewetting of a disordered melt of diblock copolymer from an ordered residual wetting layer. In contrast to simple liquids where the wetting layer has a fixed thickness and the droplets exhibit a single unique contact angle with the substrate, we find that structured liquids of diblock copolymer exhibit a discrete series of wetting layer thicknesses each producing a different contact angle. These quantized contact angles arise because the substrate and air surfaces each induce a gradient of lamellar order in the wetting layer. The interaction between the two surface profiles creates an effective interface potential that oscillates with film thickness, thus, producing a sequence of local minimums. The wetting layer thicknesses and corresponding contact angles are a direct measure of the positions and depths of these minimums. Self-consistent field theory is shown to provide qualitative agreement with the experiment.