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Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon.
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A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [Vella & Davidovitch, Phys. Rev. E 98, 013003 (2018)], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.
Complexation of polymers at liquid interfaces is an emerging technique to produce all-liquid printable and self-healing devices and membranes. It is crucial to control the assembly process but the mechanisms at play remain unclear. Using two different reflectometric methods, we investigate the spontaneous growth of H-bonded PPO-PMAA membranes at a flat liquid-liquid interface. We find that the membrane thickness h grows with time t as h~t^(1/2), which is reminiscent of a diffusion-limited process. However, counter-intuitively, we observe that this process is faster as the PPO molar mass increases. We are able to rationalize these results with a model which considers the diffusion of the PPO chains within the growing membrane. The architecture of the latter is described as a gel-like porous network, with a pore size much smaller than the radius of the diffusing PPO chains, thus inducing entropic barriers that hinder the diffusion process. From the comparison between the experimental data and the result of the model, we extract some key piece of information about the microscopic structure of the membrane. This study opens the route toward the rational design of self-assembled membranes and capsules with optimal properties.
Spider silk possesses unique mechanical properties like large extensibility, high tensile strength, super-contractility, etc. Understanding these mechanical responses require characterization of the rheological properties of silk beyond the simple force-extension relations which are widely reported. Here we study the linear and non-linear viscoelastic properties of dragline silk obtained from social spiders Stegodyphus sarasinorum using a Micro-Extension Rheometer that we have developed. Unlike continuous extension data, our technique allows for the probing of the viscoelastic response by applying small perturbations about sequentially increasing steady-state strain values. In addition, we extend our analysis to obtain the characteristic stress relaxation times and the frequency responses of the viscous and elastic moduli. Using these methods, we show that in a small strain regime (0-4%) dragline silk of social spiders shows strain-softening response followed by strain-stiffening response at higher strains (> 4%). The stress relaxation time, on the other hand, increases monotonically with increasing strain for the entire range. We also show that silk stiffens while ageing within the typical lifetime of a web. Our results demand the inclusion of the kinetics of domain unfolding and refolding in the existing models to account for the relaxation time behaviour.
In this study, we use the transient thermal grating optical technique textemdash a non-contact, laser-based thermal metrology technique with intrinsically high accuracy textemdash to investigate room-temperature phonon-mediated thermal transport in two nanoporous holey silicon membranes with limiting dimensions of 100 nm and 250 nm respectively. We compare the experimental results to ab initio calculations of phonon-mediated thermal transport according to the phonon Boltzmann transport equation (BTE) using two different computational techniques. We find that the calculations conducted within the Casimir framework, i.e. based on the BTE with the bulk phonon dispersion and diffuse scattering from surfaces, are in quantitative agreement with the experimental data, and thus conclude that this framework is adequate for describing phonon-mediated thermal transport through holey silicon membranes with feature sizes on the order of 100 nm.
We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk (three-dimensional) fluids: for rotations and motion perpendicular to the rod axis, we find purely local drag, in which the drag coefficient is purely algebraic in the rod dimensions. These results, as well as the calculational methods are applicable to such problems as the diffusion of objects in or associated with Langmuir films and lipid membranes. The methods can also be simply extended to treat viscoelastic systems.
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