Homogenization of surface energy and elasticity for highly rough surfaces

Surface energy plays a central role in several phenomena pertaining to nearly all aspects of materials science. This includes phenomena such as self-assembly, catalysis, fracture, void growth, and microstructural evolution among others. In particular, due to the large surface-to-volume ratio, the impact of surface energy on the physical response of nanostructures is nothing short of dramatic. How does the roughness of a surface renormalize the surface energy and associated quantities such as surface stress and surface elasticity? In this work, we attempt to address this question by using a multi-scale asymptotic homogenization approach. In particular, the novelty of our work is that we consider highly rough surfaces, reminiscent of experimental observations, as opposed to gentle roughness that is often treated by using a perturbation approach. We find that softening of a rough surface is significantly underestimated by conventional approaches. In addition, our approach naturally permits the consideration of bending resistance of a surface, consistent with the Steigmann-Ogden theory, in sharp contrast to the surfaces in the Gurtin-Murdoch surface elasticity theory that do not offer flexural resistance.

Structure and Undulations of Escin Adsorption Layer at Water Surface Studied by Molecular Dynamics

The saponin escin, extracted from horse chestnut seeds, forms adsorption layers with high viscoelasticity and low gas permeability. Upon deformation, escin adsorption layers often feature surface wrinkles with characteristic wavelength. In previous studies, we investigated the origin of this behavior and found that the substantial surface elasticity of escin layers may be related to a specific combination of short-, medium-, and long-range attractive forces, leading to tight molecular packing in the layers. In the current study, we performed atomistic molecular dynamics simulations of 441 escin molecules in a dense adsorption layer with an area per molecule of 0.49 nm2. We found that the surfactant molecules are less submerged in water and adopt a more upright position when compared to the characteristics determined in our previous simulations with much smaller molecular models. The number of neighbouring molecules and their local orientation, however, remain similar in the different-size models. To maintain their preferred mutual orientation, the escin molecules segregate into well-ordered domains and spontaneously form wrinkled layers. The same specific interactions (H-bonds, dipole–dipole attraction, and intermediate strong attraction) define the complex internal structure and the undulations of the layers. The analysis of the layer properties reveals a characteristic wrinkle wavelength related to the surface lateral dimensions, in qualitative agreement with the phenomenological description of thin elastic sheets.

Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.

Stability of Foams in Vacuum Drying Processes. Effects of Interactions between Sugars, Proteins, and Surfactants on Foam Stability and Dried Foam Properties

The hypothesis was that saccharides mediate interactions between surface-active components and that this will have an impact on foam decay during the drying process. Static light scattering was performed to determine changes in interactions between the foam stabilizer on a molecular level. Furthermore, pendant drop and oscillating drop measurements were performed to examine the surface tension and surface rheology. Foams were dried in conventional dryers as well as microwave-supported vacuum dryers. Final foam properties were determined. It was shown that the addition of sugars, often added as protective substances for sensitive organic molecules, resulted in lower repulsion between different types of surface-active components, namely polysorbate 80 and β-lactoglobulin (β-lg). Differences in impact of the types of sugars and between different types of surfactant, protein, and small molecules were observed influencing the foam decay behavior. The interfacial properties of polysorbate 80 and β-lg were influenced by the type of the used sugars. The surface elasticity of protein stabilized surfaces was higher compared to that of polysorbate stabilized systems. Protein stabilized systems remained more stable compared to polysorbate systems, which was also affected by the used saccharide. Overall, a correlation between molecular interactions and foam decay behavior was found.

Effect of Curvature-Dependent Surface Elasticity on the Flexural Properties of Nanowire

Surface elasticity and residual stress strongly influence the flexural properties of nanowire due to the excessively large ratio of surface area to volume. In this work, we adopt linearized surface elasticity theory, which was proposed by Chhapadia et al., to capture the influence of surface curvature on the flexural rigidity of nanowire with rectangular cross section. Additionally, we have tried to study the bending deformation of circular nanowire. All stresses and strains are measured relative to the relaxed state in which the difference in surface residual stress between the upper and lower faces of rectangular nanowire with no external load induces additional bending. The bending curvature of nanowire in the reference and relaxed states is obtained. We find that flexural rigidity is composed of three parts. The first term is defined by the precept of continuum mechanics, and the last two terms are defined by surface elasticity. The normalized curvature increases with the decrease in height, thereby stiffening the nanowire. We also find that not only sizes but also surface curvature induced by surface residual stress influence the bending rigidity of nanowire.

Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

This paper deals with the investigation of nonlinear static pull-in instability of smart Nano-switches regarding the new size-dependent phenomenon, known as flexoelectricity, together with the surface effects. It is noteworthy that the coupling effect of the flexoelectricity and surface elasticity on nonlinear static pull-in instability of electrostatically-actuated Nano-switches has not been studied before. Euler-Bernoulli beam assumptions in conjunction with the von-Karman nonlinearity are considered to formulate the problem. The Nano-switch is subjected to electrostatic actuation force with fringing field effect as well as Casimir force. Refined constitutive relations for piezoelectric materials capturing the flexoelectric effects are taken into consideration for mathematical modeling. Additionally, a surface elasticity approach is employed to reach an accurate model for the system. Considering the imposed electric boundary conditions, Gauss’s equation is solved to acquire the electric potential distribution along with the thickness of the Nano-switch. Thereafter, Hamilton’s principle is hired to derive the coupled nonlinear governing equations of the system. Utilizing the differential quadrature method (DQM), the nonlinear ordinary differential equations are transformed into a system of nonlinear algebraic equations. Consequently, Newton-Raphson method is exploited as a numerical method to solve the obtained algebraic equations which leads to the pull-in voltage. Investigating the maximum displacement of the Nano-switch in response to the applied electrostatic force, the effects of various involved parameters such as flexoelectricity and surface elasticity on pull-in instability are explored in detail. Furthermore, the size-dependent behavior of the pull-in instability against the flexoelectric, surface effects and applied piezoelectric voltage is analyzed. Totally, it is revealed that the flexoelectricity may exhibit a substantial influence on the pull-in behavior of smart Nano-switches, especially for some cases with small thicknesses. Therefore, this effect should be taken into account to reach an accurate, reliable and optimized design for Nano-switches.