Mark Ilton

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.

Symmetry plays a key role in the erasing of patterned surface features

We report on how the relaxation of patterns prepared on a thin film can be controlled by manipu- lating the symmetry of the initial shape. The validity of a lubrication theory for the capillary-driven relaxation of surface profiles is verified by atomic force microscopy measurements, performed on films that were patterned using focused laser spike annealing. In particular, we observe that the shape of the surface profile at late times is entirely determined by the initial symmetry of the perturba- tion, in agreement with the theory. Moreover, in this regime the perturbation amplitude relaxes as a power-law in time, with an exponent that is also related to the initial symmetry. The results have relevance in the dynamical control of topographic perturbations for nanolithography and high density memory storage.

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

Hop, skip, jump, or massive leap In biological and engineered systems, an inherent trade-off exists between the force and velocity that can be delivered by a muscle, spring, or combination of the two. However, one can amplify the maximum throwing power of an arm by storing the energy in a bow or sling shot with a latch mechanism for sudden release. Ilton et al. used modeling to explore the performance of motor-driven versus spring-latch systems in engineering and biology across size scales. They found a range of general principles that are common to animals, plants, fungi, and machines that use elastic structures to maximize kinetic energy. Science, this issue p. eaao1082 Combining motors, springs, and latches offers many routes to optimization of mechanical power in biological and engineered systems. INTRODUCTION Mechanical power, whether for launched missiles or running humans, is limited by the universal, physical trade-off between force and velocity. However, many biological systems use power-amplifying mechanisms that enable unmatched accelerations in challenging environments and across a wide range of size scales. How these mechanisms actually enhance power output remains unclear. Power-amplified biological systems are of particular interest because they achieve a trio of combined capabilities that exceed current engineering performance: (i) high accelerations that (ii) can be continuously fueled through metabolic processes and (iii) are used repeatedly with minimal performance degradation throughout the life of the organism. Although engineers have struggled to design lightweight and long-lasting devices that can deliver high power output, biological systems have been performing such feats for millions of years and using these systems for a myriad of functions. RATIONALE Through a mathematical analysis that is equally applicable to biological and synthetic systems, we investigate how power enhancement emerges through the dynamic coupling of motors, springs, latches, and projectiles and relate the findings to data on existing biological and engineered systems. The model incorporates nonideal behavior of spring and latch systems in a scalable framework using both dimensional and dimensionless approaches. RESULTS Motors, springs, and latches all experience force-velocity trade-offs, and their integration exemplifies the cascading effects of power limits. Springs circumvent motor power limits when projectile mass is small and the motor’s force-velocity dynamics limit performance. However, springs also exhibit force-velocity trade-offs when their mass, mechanical properties, and time dependence are incorporated. Latches dynamically modulate spring power through variation in latch shape and velocity. Motor-driven and spring-driven movements are distinct in their transitions across performance (power, maximum velocity, and duration), which are largely dictated by projectile mass. When analyzed as a single, integrated system, the necessity for tuning and inherent tunability are evident. Simply increasing the force output of a motor does not enhance performance; the spring and latch capacities must also shift. Simply decreasing the size of the system also does not enhance performance; spring energy storage falls off at smaller scales due to the effects of materials, stiffness, and geometry. With this mathematical foundation of scaling and integration, we apply a new lens to patterns of biological scaling limits and propose new design principles for integrated and tuned systems. CONCLUSION Our model reveals a foundational framework for the scaling, synthetic design, and evolutionary diversification of power-amplified systems. The model enables a straightforward approach to analyzing biological systems, encourages a rich design space and functionality for synthetic systems, and highlights a compelling need for the integrative analysis of spring and latch dynamics in both synthetic and biological systems. Power-amplified biological and synthetic systems use spring elements to drive motion over a range of size scales. Mathematical modeling reveals a cascade of power limits and mass-dependent transitions in power delivery that arise from the integration of motors, springs, and latches to actuate movement. Variation of these components creates synergistic effects relevant to the analysis and synthesis of diverse power-amplified 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.When modeling fluid flow over a solid surface, one must determine the slip velocity at the boundary. Here Ilton et al. perform experiments to quantify the slip length of polymer melts at a nearly ideal solid surface and capture them in a model involving the density of physically adsorbed polymer chains.

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.