Mechanical Self-Assembly

Mother Nature provides unlimited inspirations of ordered patterns across vast scales: from the helical DNA and lipid bilayers at the submicron level, to the skin and tissue wrinkle at the millimeter level, to the ordered shapes in plants and animals at the meter level, and to the geological features at the mega scale. Many of these intriguing patterns are underpinned by mechanics-driven processes, including spontaneous buckling deformation.

Morphogenesis, as one of the three fundamental aspects of developmental biology, refers to the biological processes of developing certain shapes, which takes place across many length scales, including the morphologies of a cell, a tissue, an organ, and a system. From the intrinsic yet complicated biological and biochemical perspectives, several mechanisms for plant pattern formation have been suggested, such as positional information theory [1] and reaction–diffusion theory [2]. However, the active role of mechanical forces should not be underemphasized.

In the past few years, a great interest has been sparked in the development of biophysical and mechanical theories to explain the plant pattern formation [3, 4]. Among them, the connection of the morphogenetic processes of some plants with mechanical buckling theory receives a great attraction owing to some similarities. Patterns and shape formation are treated as the generation of specific undulating physical topography. From biophysical viewpoints, during the growth of plants, the morphology transition can be treated as spontaneously approaching the pattern/mode with minimal energy, which is similar to the mechanical instability/bifurcation approach. Among the several possible buckling/wrinkling modes (i.e., undulating patterns or structures), the system will spontaneously choose the pattern with the minimized energy.

One shaping method of soft elastic bodies is growth. This method, which is very common in natural systems and much less in man-made structures, is inherently different from shaping by external loading. In the second case the body responses passively to the constraints imposed on its boundaries. It has a reference stress-free configuration and the task is to compute and minimize the elastic energy of configurations that fulfill the boundary conditions. In the case of self-shaping by growth, the body is free in space, but contains a field of active growth, or deformation, which determines the shape of the body.

Instability of a stiff thin film attached to a compliant substrate generally results in the appearance of exquisite wrinkles with length scales that depend on the system geometry and applied stresses. Several methods have been developed for creating surface wrinkles including inducing compressive stresses/strains on a thin metal deposited on a polymer substrate, dewetting polymer, and UVO/ion beam-irradiated polymeric surface.

In this work, we have reviewed the formation of ion beam-induced self-assembled wrinkle patterns on polymer surfaces. Exposure to ion beam generally results in formation of a stiff skin on surface areas of a polymeric surface. The created stiff skin has strain mismatch with the polymeric surface, leading to generation of ordered surface wrinkles. By controlling the ion beam fluence and area of exposure of the poly(dimethylsiloxane) (PDMS), one can create a variety of patterns in the wavelengths in the micron to submicron range, from simple one-dimensional wrinkles to peculiar and complex hierarchical nested wrinkles. The induced strains in the stiff skin can be estimated by measuring the surface length in the buckled state. The patterned surfaces have a variety of cross-disciplinary applications that range from optics and electronics to tissue engineering and regenerative medicine. One novel usage of these patterns is for fabricating wrinkles with extreme topology. As an example, by using the prefabricated wrinkle pattern by ion beam, we developed wrinkles with high aspect ratio of amplitude over wavelength. Here, first the wrinkles were induced on a PDMS surface using Ar ion beam irradiation. The wrinkles had a wavelength in the range of 200–1,400nm depending on the ion treatment time. Then, an amorphous carbon film was deposited on the pre-patterned PDMS to elevate the amplitude of surface features using a glancing angle deposition.

Complex wrinkle patterns have been observed in various thin film systems, typically with integrated hard and soft materials for various applications as well as in nature. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. On an elastic substrate, equilibrium and energetics set the critical condition and select the wrinkle wavelength and amplitude. On a viscous substrate, wrinkles grow over time and kinetics select the fastest growing mode. Moreover, on a viscoelastic substrate, both energetics and kinetics play important roles in determining the critical condition, the growth rate, and wrinkle patterns. The dynamics of wrinkling, while analogous to other phase ordering phenomena, is rich and distinct under the effects of stress and film–substrate interactions. In this chapter, a kinetics approach is presented for wrinkling of isotropic and anisotropic elastic films on viscoelastic substrates. Analytic solutions are obtained by a linear perturbation analysis and a nonlinear energy minimization method, which predict the kinetics of wrinkle growth at the early stage and the equilibrium states at the long-time limit, respectively. In between, a power-law coarsening of the wrinkle wavelength is predicted by a scaling analysis. Furthermore, the kinetics approach enables numerical simulations that demonstrate emergence and transition of diverse wrinkle patterns (ordered and disordered) under various conditions.

Crease instability takes place on the surface of a solid when the lateral compression exceeds a critical level. Despite the weak singularity at the cusp, formation of a crease relieves the elastic energy through the local out-of-plane deformation. Due to the singular fields of deformation and stress, a crease differs from wrinkles in both appearance and mathematical description. The singularity also prevents common linearization-based methods for stability analysis from correctly predicting the critical condition for the instability. This chapter first reviews the recently published energy method which has successfully calculated the critical strain for crease formation. Examples of more general loading conditions, such as the crease instability on growing tissues, are demonstrated. Moreover, the equilibrium states of a crease on a film of finite thickness are studied. The approach of extrapolating the results of thinner films actually yields a more accurate result than the energy method. With the aid of this new approach, the later part of the chapter focuses on the effect of material properties on crease instabilities. The effect of material compressibility, as well as the crease formation on a swelling gel, is further investigated.

The aim of this chapter is to review the studies on buckle delamination in compressively stressed thin films over substrates by pulling together experimental and theoretical analysis. The general phenomena shown in delamination buckles of compressively stressed films were discussed from the onset to propagation over the substrates. The experimental observations were characterized by the delamination conditions and buckle morphologies. Then, the related mechanics for buckle delamination were provided with a theoretical solution for simple buckle configurations and a numerical solution for nonlinear buckle. Based on the experimental and theoretical analysis, the buckle configuration was applied to fluidic channels by precisely controlling buckle width within the desired area by adjusting interface adhesion.

This chapter describes the method of manufacturing microfluidic microchannels formed by delaminated buckled thin films. Thin films under compression tend to delaminate and buckle. Microchannel geometry can be controlled by tailoring film residual stress and placing patterned adhesion-weakening layers utilizing photolithographic techniques. Results based on the photoresist as the adhesion weakening layer and compressed tungsten thin films are described along with the corresponding thin film mechanics.

Self-assembled buckling patterns of thin films on compliant substrates have been subjected to extensive studies and shown great promise in micro-fabrication. However, most previous studies were limited to planar substrates, and the study of buckling of films on curved substrates has not received sufficient attention. With the constraining effect from various types of substrate curvature, numerous new types of buckling morphologies may emerge which not only enable true three-dimensional (3D) fabrication of microstructures and microdevices but also have important implications for the morphogenesis of quite a few natural and biological systems. We review the scientific aspects of elastic buckling of thin films on several representative curved substrates, emphasizing the critical effect of substrate curvature, its interaction with other material/system parameters, and ways to control the buckles based on mechanical and physical principles and bridge them with prospect applications in biology, biomedical engineering, and small-scale fabrication.