The primary objective of this article is twofold: to address the key concept of topology that impacts materials science in a major way and to convey the excitement to the materials community of recent significant advances in our understanding of the important topological notions in a wide class of materials with potential technological applications. A paradigm of topology/geometry → property → functionality is emerging that goes beyond the traditional microscopic structure → property → functionality relationship. The new approach delineates the active roles of topology and geometry in design, fabrication, characterization, and predictive modeling of novel materials properties and multifunctionalities. After introducing the essentials of topology and geometry, we elucidate these concepts through a gamut of nanocarbon allotropes of de novo carbons, hierarchical self-assembled soft- and biomaterials, supramolecular assemblies, and nanoporous materials. Applications of these topological materials range from sensing, energy storage/conversion, and catalysis to nanomedicine.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6504594F89AA0E00BC60A8AADB2B8613/S0883769414000281a.pdf/div-class-title-a-topological-twist-on-materials-science-div.pdf

A topological twist on materials science

We have carried out a systematic study of buckling-like mechanical instabilities in simple two- (2D) and three-dimensional (3D) symmetric foam clusters sandwiched between parallel planar walls. These instabilities occur when the wall separation w is reduced below a critical value, w*, for which the foam surface energy E reaches its minimum, E*. The clusters under investigation consist of either a single bubble, or of “twin bubbles” of fixed equal sizes (areas A in 2D or volumes V in 3D), which are either free to slide or pinned at the confining walls. We have numerically obtained w* for both free and pinned 2D and 3D clusters. Furthermore, we have calculated the buckled configurations of 2D twin bubbles, either free or pinned, and of 3D free twin bubbles, whose energy is independent of w and equal to the minimum energy E* of the unbuckled state. Finally, we have also predicted the critical wt* at which the terminal configurations under extension of 2D and 3D single and twin bubbles are realised. Experimental illustrations of these transitions under compression and extension are presented. Our results, together with others from the literature, suggest that a bubble cluster bounded by two parallel walls is stable only if the normal force it exerts on the walls is attractive, i.e., if dE/dw > 0; clusters that cause repulsion between the walls are unstable. We correlate this with the distribution of film orientations: films in a stable cluster cannot be “too parallel” to the confining walls; rather, their average tilt must be larger than for a random distribution of film orientations.

Mechanical instabilities of bubble clusters between parallel walls

The aim of this article is to provide a general introduction to the fascinating world of liquid foams for non-specialists and to establish the general background for a comprehensive understanding of the papers that compose this special issue. Liquid foams are cellular materials composed of gas bubbles surrounded by a continuous liquid film. Although this article focuses on the main aspects of liquid foams, detailed attention will be given to the topics that Professor Manuel Amaral Fortes devoted his time.

Liquid foams: an introduction

/pdf/instabilities-in-two-dimensional-flower-and-chain-clusters-1s0u5ogrzs.pdf

Instabilities in two-dimensional flower and chain clusters of bubbles

We report experiments on soap film configurations in a triangular prism for which the shape factor can be changed continuously. Two stable configurations can be observed for a range of the shape factor $h$, being the prism-height/edge-length ratio. A hysteretic behavior is found, due to the occurence of another local minima in the free energy. Contrary to a common belief, soap films can be trapped in a particular configuration being different from a global surface minimization. This metastability can be evidenced from a geometrical model based on idealized structures. Depending on the configuration, the transition is either first or second order, providing clues on the structural relaxations taking place into three-dimensional foams, such as T1 rearrangements.

Hysteretic behavior in three-dimensional soap film rearrangements.

We present an experimental and theoretical investigation of a system composed of two soap bubbles strained between two parallel solid surfaces. The two-bubble cluster can be found in several configurations. The existence and stability of each of these states is studied as a function of the distance between the two facing surfaces. The change of this distance can induce a transition from one configuration to another; we observe that most transitions are subcritical, showing that the system is often trapped in states where the minimum of free energy is only local. The hysteretic transitions are responsible for the dissipation of elastic energy. The existence of more than one stable states for given boundaries conditions combined with the absence of thermalization means that the history of the system has to be taken into account and that there is no unique stress-strain relation. In the present system, because of its simplicity, a complete quantitative analysis of these general processes is obtained. The presented results may contribute to a better understanding of the dynamics of more complex systems such as foams or granular materials where similar processes are at work.

http://asterion.rockefeller.edu/steffen/Bus.pdf

Bubbles under stress.

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Bubbles under stress.