Geometric control of tilt transition dynamics in single-clamped thermalized elastic sheets.

We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane above or below the horizontal. The resultant thermally roughened two-state (up/down) system possesses rich dynamics on multiple timescales. In the tilted regime a finite-energy barrier separates the spontaneously chosen up state from the inversion-symmetric down state. Molecular dynamics simulations confirm that, over sufficiently long time, such thermalized elastic sheets transition between the two states, residing in each for a finite dwell time. One might expect that temperature is the primary driver for tilt inversion. We find, instead, that the primary control parameter, at fixed tilt order parameter, is the dimensionless and purely geometrical aspect ratio of the clamped width to the total length of the otherwise-free sheet. Using a combination of an effective mean-field theory and Kramers' theory, we derive the transition rate and examine its asymptotic behavior. At length scales beyond a material-dependent thermal length scale, renormalization of the elastic constants qualitatively modifies the temperature response. In particular, the transition is suppressed by thermal fluctuations, enhancing the robustness of the tilted state. We check and supplement these findings with further molecular dynamics simulations for a range of aspect ratios and temperatures.

Anomalous Thermal Expansion in Ising-like Puckered Sheets.

Motivated by efforts to create thin nanoscale metamaterials and understand atomically thin binary monolayers, we study the finite temperature statistical mechanics of arrays of bistable buckled dilations embedded in free-standing two-dimensional crystalline membranes that are allowed to fluctuate in three dimensions. The buckled nodes behave like discrete, but highly compressible, Ising spins, leading to a phase transition at T_{c} with singularities in the staggered "magnetization," susceptibility, and specific heat, studied via molecular dynamics simulations. Unlike conventional Ising models, we observe a striking divergence and sign change of the coefficient of thermal expansion near T_{c} caused by the coupling of flexural phonons to the buckled spin texture. We argue that a phenomenological model coupling Ising degrees of freedom to the flexural phonons in a thin elastic sheet can explain this unusual response.

Erratum: Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning [Phys. Rev. Lett. 121, 255304 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.255304.

Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning.

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ∼4×10^{6} candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

Kirigami actuators.

Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single non-propagating crack in a sheet, we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments on centimeter-scale objects and molecular dynamics simulations of graphene and MoS2 nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators.

Highly stretchable MoS2 kirigami.

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS2 kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key findings are significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS2 nanoribbons. These results, in conjunction with recent results on graphene, suggest that the kirigami approach may be generally useful for enhancing the ductility of two-dimensional nanomaterials.

A unifying framework to quantify the effects of substrate interactions, stiffness, and roughness on the dynamics of thin supported polymer films.

Changes in the dynamics of supported polymer films in comparison to bulk materials involve a complex convolution of effects, such as substrate interactions, roughness, and compliance, in addition to film thickness. We consider molecular dynamics simulations of substrate-supported, coarse-grained polymer films where these parameters are tuned separately to determine how each of these variables influence the molecular dynamics of thin polymer films. We find that all these variables significantly influence the film dynamics, leading to a seemingly intractable degree of complexity in describing these changes. However, by considering how these constraining variables influence string-like collective motion within the film, we show that all our observations can be understood in a unified and quantitative way. More specifically, the string model for glass-forming liquids implies that the changes in the structural relaxation of these films are governed by the changes in the average length of string-like cooperative motions and this model is confirmed under all conditions considered in our simulations. Ultimately, these changes are parameterized in terms of just the activation enthalpy and entropy for molecular organization, which have predictable dependences on substrate properties and film thickness, offering a promising approach for the rational design of film properties.

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials.

The study of glass formation is largely framed by semiempirical models that emphasize the importance of progressively growing cooperative motion accompanying the drop in fluid configurational entropy, emergent elasticity, or the vanishing of accessible free volume available for molecular motion in cooled liquids. We investigate the extent to which these descriptions are related through computations on a model coarse-grained polymer melt, with and without nanoparticle additives, and for supported polymer films with smooth or rough surfaces, allowing for substantial variation of the glass transition temperature and the fragility of glass formation. We find quantitative relations between emergent elasticity, the average local volume accessible for particle motion, and the growth of collective motion in cooled liquids. Surprisingly, we find that each of these models of glass formation can equally well describe the relaxation data for all of the systems that we simulate. In this way, we uncover some unity in our understanding of glass-forming materials from perspectives formerly considered as distinct.

Interfacial mobility scale determines the scale of collective motion and relaxation rate in polymer films.

Thin polymer films are ubiquitous in manufacturing and medical applications, and there has been intense interest in how film thickness and substrate interactions influence film dynamics. It is appreciated that a polymer-air interfacial layer with enhanced mobility plays an important role in the observed changes and recent studies suggest that the length scale ξ of this interfacial layer is related to film relaxation. In the context of the Adam-Gibbs and random first-order transition models of glass formation, these results provide indirect evidence for a relation between ξ and the scale of collective molecular motion. Here we report direct evidence for a proportionality between ξ and the average length L of string-like particle displacements in simulations of polymer films supported on substrates with variable interaction strength and rigidity. This relation explicitly links ξ to the theoretical scale of cooperatively rearranging regions, offering a promising route to experimentally determine this scale of cooperative motion.

Local variation of fragility and glass transition temperature of ultra-thin supported polymer films.

Despite extensive efforts, a definitive picture of the glass transition of ultra-thin polymer films has yet to emerge. The effect of film thickness h on the glass transition temperature T(g) has been widely examined, but this characterization does not account for the fragility of glass-formation, which quantifies how rapidly relaxation times vary with temperature T. Accordingly, we simulate supported polymer films of a bead-spring model and determine both T(g) and fragility, both as a function of h and film depth. We contrast changes in the relaxation dynamics with density ρ and demonstrate the limitations of the commonly invoked free-volume layer model. As opposed to bulk polymer materials, we find that the fragility and T(g) do not generally vary proportionately. Consequently, the determination of the fragility profile--both locally and for the film as a whole--is essential for the characterization of changes in film dynamics with confinement.