Material Organization in nature

Material organization in nature

Biotechnology materials

Material organization in nature - Advanced Sustainability

The Role of Mechanics in Biological and Biologically Inspired Materials In the development of new materials, researchers have recently turned to nature for inspiration and assistance. A special emphasis has been placed on understanding the development of biological materials from the traditional correlation of structure to property, as well as correlating structure to functionality. The natural evolution of structure in biological materials is guided by the interaction between these materials and their environment. What is most notable about natural materials is the way in which the structure is able to adapt at a wide range of length scales. Much of the interaction that biological materials experience occurs through mechanical contact. Therefore, to develop biologically inspired materials it is necessary to quantify the mechanical behavior of and mechanical influences on biological structures with the intention of defining the natural structureproperty- functionality relationship for these materials.

Near the end of the twentieth century, a new focus was placed on microtechnology and nanotechnology. This was predicated on new characterization technologies, such as atomic force microscopy, that enabled visualization of natural phenomena down to the atomistic scale, as well as microtensile testers and nanoindenters

for microscale and nanoscale mechanical characterization. At these size scales, new natural phenomena were revealed that presented scientists and engineers with a novel approach to engineering materials and structures.

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Biomimetics Biomimetics refers to human-made processes,substances, devices, or systems that imitate nature, and has led to the development of new biologically inspired materials based on biological analogs. The research in this area can either be focused on the investigation of natural materials, or on the processes that optimize the structure of materials in a manner similar to that occurring in nature. Therefore, biology can become the basis for developing new processes required for synthesizing materials, while mechanics can be used to interpret the manner in which the properties and functionality associated with the structure of natural materials have enabled them to adapt to environmental stimuli.

For the most part, the science and engineering of synthetic materials have been separated into classes of structures, length scales and functionality that are used to differentiate disciplines such as experimental mechanics and materials science from each other. However, biological materials do not conform to disciplinary boundaries, since they possess structures that span across a full range of length scales in order to react to a variety of environmental stimuli with optimal functionality. A number of technological breakthroughs may be achieved through mimicry of the multi-scale optimization of structure and Each process is examined for mechanisms, scale functionality in natural materials, such as material of effect, and opportunity for creative human systems with morphogenesis capabiiities and intervention or utilization. bimorphic explorer robots with versatile mobility.

Learning from and mastering Nature's concepts The translation of this multi-scale optimization of not only satisfies humankind's insatiable curiosity structure and functionality to the science of for understanding the world around us, but also advanced materials is a part of the new field where promises to drive a paradigm shift in modern science and engineering are joined together: materials science and technology. biomimetics.

Material organization in nature - Advanced Sustainability

Fibrous Tissues

Mechanics of helical structures

One of the most ubiquitous of biological materials is fibrous tissue, which is an aggregate of cells characterized by a helical fibrous structure. The mechanics of fibrous tissues has become of interest recently because the peculiar mechanical characteristics of tissues within an organism are tailored to their specific functional needs, both by the properties of the constituent "building blocks" and their structural organization.

Thus, they tend to have a hierarchical structure and very often they have helical fibers in one or more levels within their hierarchy.

Helical fibers can be tailored to suit the mechanical environment by nature of relative fiber movements caused by realignment of fibers within the helix.

These movements can be controlled by the interfiber force, which is related to the helix angle, and the nature of solid or viscous friction between the fibers, or by the shear modulus of a solid matrix.

Although there is a huge range of biological fibrous structures, all come from a small number of building blocks in terms of fibers and matrix materials (or ground substances). The main fibrous building blocks are broadly polypeptides in mammalian structures (e.g., collagen and elastin) and polysaccharides in plant structures and insects (e.g., chitin and cellulose). The matrix materials are globular proteins or glycoproteins and water in uncalcified soft tissues. In hard tissues, hydroxyapitite and lignin are the most common matrix/filler materials. The small variation in the basic components of biological materials implies that the large variations in observed properties are the direct result of structural variations.

This leads to a very versatile range of mechanical properties governing flexibility, damage tolerance, energy absorption, and linear force-pressure actuation that are dictated by the nature of the inter-fiber forces. Inter-fiber forces arise because the asymmetrical nature of a helix it will tend to try and unwind and straighten out when loaded along its long axis. Often practical constraints exist which prevent the helix from unwinding. For example, other helical fibers may be wound in the same and opposite direction. In this case, forces will develop between different fibers that are a function of the geometry and can be given approximately with simple formulae.

There is a great deal of interest in developing more complex mechanical models that can take into account additional factors, such as geometrical changes during loading, bending, twisting and frictional effects.

The geometry of helical structures also results in a

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high axial strength and a low bending stiffness. As a helical fiber oscillates from tension at the top to compression at the bottom of a "strand," and if the fibers can slide (because they are embedded in a viscous material), then the second moment of area of a bundle of fibers, will change dramatically.

The nature of the fiber bundle gives rise to another advantage in terms of damage tolerance: crack isolation. Given a sufficiently weak interface between fibers, a crack will not pass from one fiber to the next. Additionally, because of lateral forces between fibers caused by the helix structurepulling itself together in tension, a break in the fiber will gradually take up the load until at some distance from the break it regains its full share of the load. In contrast to a simple actually a force between the fibers this mechanism will occur even if the interface between the fibers is a viscous fluid or nothing (i.e., relying on inter-fiber frictional forces).

Fibrous bundles are also capable of absorbing tremendous amounts of energy. Using the interfiber shear mechanism, a tensile structure can be designed with significant levels of hysteresis within a load cycle, which may be time-dependent viscoelastic behavior (in the case of a viscous fluid interface) or time-independent Coulomb-type damping (for a frictional interface).

Material organization in nature - Advanced Sustainability

Examples in Nature

component were made of a truly tree-like material, the material would be adapted across length scales for the application as well as for the location within the structure. In one location of a part, the material could emphasize fracture toughness.

Wood is another ubiquitous biological material that represents adaptation of a plant species to exploit an ecological niche through a multi-scale structure. Wood makes use of a variety of helical structures to create a structure that has both stiffness and strength adapted to ecological needs and represents a genetic adaptation to the success of a particular competitive strategy for growth.

For example, early in the life of the tree the wood emphasizes the need to grow quickly and compete for light. Later in life, wind and other environmental loads pose the greatest risk to the tree. The mature wood that is produced is therefore stronger, but less height results from the energy investment. Both the molecular structure and the physical orientation of the structural elements adapt, as a result of the changing needs during growth.

The engineering equivalent of this approach would require that not only the shape of a component be designed for an application, but the structure of the material at the microscopic and the molecular level would adapt for each application as well. The engineering equivalent to adaptation during the life would be in-service changes in the material.

So, for example, if the structure of an engineered

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Fracture toughness might gradually become less important in another area where greater strength would be required. Springs or mounting points could be integrated into a single part by simply adapting the modulus. In the case of a composite material, this type of design could be implemented by orienting the polymer chains or crystallinity in the matrix structures, as well as by varying the percentage of reinforcement.

The geometry of a right hand helix, where ct is the helix angle. For one full rotation of the helix ~R = 2~R and b = S (the pitch). The radius of curvature of a helix can be shown to be: K = sin2 Îą R

Multi-scale structure of wood

To fully implement the biomimicry of wood,the material would have to adapt to the application.

So, if a system encountered unexpected loading in use, the material would adapt to the new loading by emphasizing the need for increased strength or modulus. The environment would trigger active control and dynamic repair. The biological world can provide inspiration and direction for developing this type of integrated system and material design. Additionally, the design process can mimic the genetic adaptation to environmental demands for the development of shape and materials for a particular application. Furthermore, it is notable that wood serves not only as a structural material for the tree.

Case I - Material organization of the Euplectella marine sponge

Material organization in nature - Advanced Sustainability

Hierarchically assembled fibrous material Nature fascinates scientists and engineers with numerous examples of exceptionally strong building materials. These materials often show complex hierarchical organization from the nanometer to the macroscopic scale. Every structural level contributes to the mechanical stability and toughness of the resulting design.

For instance, the subtle interplay between the lattice structure, fibril structure, and cellulose is responsible for the remarkable properties of wood. In particular,it consists of parallel hollow tubes, the wood cells, which are reinforced by nanometer thick cellulose fibrils wound helically around the cell to adjust the material as needed Deformation occurs by shearing of a matrix rich in hemicelluloses and lignin, “ gluing� neighboring fibrils, and allowing a stick-slip movement of the fibrils. Wood is an example that shows the wide range of mechanical performance achievable by constructing with fibers.

Bone is another example of a hierarchically assembled fibrous material. Its strength critically depends on the interplay between different structural levels— from the molecular/nanoscale interaction between crystallites of calcium phosphate and an organic framework, through the

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micrometer-scale assembly of collagen fibrils, to the millimeter level organization of lamellar bone.

mechanical protection of diatom cells was suggested to arise from the increased strength of their silica frustules.

Whereas wood is fully organic material, bone is a composite, with about half organic and half mineral components tightly interconnected at the nanoscale. However, nature has also evolved almost pure mineral structures, which - despite the inherent brittleness of most minerals- are tough enough to serve as protection for the organism.

Material organization of the Euplectella sp.

In mollusk nacre, for example, the toughening effect is due to well-defined nanolayers of organics at the interfaces between microtablets of calcium carbonate. In such structures, the stiff components (usually mineral) absorb the bulk of the externally applied loads. The organic layers, in turn, provide toughness, prevent the spread of the cracks into the interior of the structure, and even confer a remarkable capacity for recovery after deformation (13).

Spicules in siliceous sponges Glass is widely used as a building material in the biological world, despite its fragility. Organisms have evolved means to effectively reinforce this inherently brittle material. It has been shown that spicules in siliceous sponges exhibit exceptional flexibility and toughness compared with brittle synthetic glass rods of similar length scales. The

The Euplectella sp. is a deep-sea, sedimentdwelling sponge from the Western Pacific.

Sponges are now among the central artifacts in an emerging branch of science: biomimetics. That's the study of whatever nature does well - and how that may inspire better tools, materials, and processes. Harvard physical chemist Joanna Aizenberg is particularly interested in how living organisms form robust and elegant inorganic structures. The glass fibers framing those deepsea sponges, for instance, are stronger and more optically efficient than anything humankind can yet make.

Structural properties of biosilica were observed in the hexactinellid sponge Euplectella sp.

Consolidated, nanometer-scaled silica spheres are arranged in well-defined microscopic concentric rings glued together by organic matrix to form laminated spicules.

The assembly of these spicules into bundles, effected by the laminated silica-based cement, results in the formation of a macroscopic

Material organization in nature - Advanced Sustainability

cylindrical square-lattice cagelike structure reinforced by diagonal ridges.

provide additional structural benefits to this unique glass skeletal system.

The ensuing design overcomes the brittleness of its constituent material, glass, and shows outstanding mechanical rigidity and stability. The glass fibers framing those deep-sea sponges, for instance, are stronger and more optically efficient than anything humankind can yet make.

The images of the skeleton of Euplectella sp., show the intricate,cylindrical cagelike structure (20 to 25 cm long, 2 to 4 cm in diameter) with lateral (“ oscular� ) openings (1 to 3 mm in diameter). The diameter of the cylinder and the size of the oscular openings gradually increase from the bottom to the top of the structure. The basal segment of Euplectella sp. is anchored into the soft sediments of the sea floor and is loosely connected to the rigid cage structure, which is exposed to ocean currents and supports the living portion of the sponge responsible for filtering and metabolite trapping (23, 24). The characteristic sizes and construction mechanisms of the Euplectella sp. skeletal system are expected to be fine-tuned for these functions.

The individual spicules are, however, just one structural level in a highly sophisticated, nearly purely mineral skeleton of this siliceous sponge.

The assembly of a macroscopic, mechanically resistant cylindrical glass cage is possible in a modular, bottom-up fashion comprising at least seven hierarchical levels, all contributing to mechanical performance. These include silica nanospheres that are arranged into concentric layers separated from one another by alternating organic layers to yield lamellar fibers.

The fibers are in turn bundled and organized within a silica matrix to produce flexurally rigid composite beams at the micron scale. The macroscopic arrangement of these beams in a rectangular lattice with ancillary crossbeams is ideal for resisting tensile and shearing stresses.

Finally, we identify various structural motifs that

At the macroscale, the cylindrical structure is reinforced by external ridges that extend perpendicular to the surface of the cylinder and spiral the cage at an angle of 45. The pitch of the external ridges decreases from the basal to the top portion of the cage. The surface of the cylinder consists of a regular square lattice composed of a series of cemented vertical and horizontal struts, each consisting of bundled spicules aligned parallel to one another, with diagonal elements positioned in every second square cell.

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Material organization in nature - Advanced Sustainability

These layers are arranged in a cylindrical fashion around a central proteinaceous filament and are separated from one another by organic interlayers.

Etching of spicule layers and the surrounding cement showed that at the nanoscale the fundamental construction unit consists of consolidated hydrated silica nanoparticles (50 to 200 nm in diameter). The different levels of structural complexity are schematically shown in.

In the following discussion, each hierarchical level is examined from the mechanical perspective.

The first level is biologically produced glass composed of consolidated silica nanospheres formed around a protein filament. Glass as a building material suffers primarily from its brittleness. This means that its strength is limited mostly by surface defects where the applied stresses concentrate.

A scratch in the surface of glass readily induces fracture. If we consider that surface defects in the biosilica may be induced by external point loads, either biologically or otherwise applied, a scratched plain glass spicule would lose most of its strength and would fracture when subsequently loaded in tension or bending.The intrinsically low strength of the glass is balanced at the next structural level. The spicule as a whole can be regarded as a laminated composite in which the organic interlayers act as crack stoppers. If a

Fragment of the cage structure showing the square-grid lattice of vertical and horizontal str uts with diagonal elements arranged in a chessboard manner.

Scanning electron micrograph showing that each strut is composed of bundled multiple spicules (the arrow indicates the long axis of the skeletal lattice). Scale bar, 100 mm.

point load is applied to the surface, one may expect that the damage will be restricted to the outermost layers. A larger number of individual glass layers should protect the spicule more effectively from this type of damage. Thin organic interlayers seem also to be important to prevent cracks from propagating to inner layers under the influence of indentation. The observed decrease of the silica layer thickness from the spicule core to the periphery is likely to provide an additional reinforcement to the spicules. Thicker inner layers help enhance mechanical rigidity of the spicule, whereas the thinner outer layers effectively limit the depth of crack penetration.In a further level of hierarchy, spicules are joined into parallel bundles, a well-known construction principle in ceramic materials. Generally, a bundle of fibers with slightly different strength will have a much larger defect tolerance (and, therefore, strength) than each of the individual fibers.

Indeed, if one fiber fails (e.g., under tension), neighboring ones still hold, and the crack in the first fiber will be deflected at the interface to its neighbors (or at the interface between the fiber and cement). A weak lateral bonding between fibers (or between fiber and matrix) is essential for this toughening mechanism to work.The bundled spicules are arranged horizontally and vertically into a square-grid cylindrical cage reinforced by ancillary diagonal fibers running in both directions.

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E) SEM of the HF-etched (25) junction area showing that the lattice is cemented with laminated silica layers. Scale bar, 25 mm. (F) Contrast-enhanced SEM image of a cross section through one of the spicular struts, revealing that they are composed of a wide range of differentsized spicules surrounded by a laminated silica matrix. Scale bar, 10 mm.

Material organization in nature - Advanced Sustainability

Theoretical analyses of strut structures have shown that when the number of struts per node, Z, exceeds a certain value, the structure is stable even if the nodes can rotate freely. Deshpande et al. have given the stability limit as Z ≥ 6 ( D - 1 ) for grids in D = 2 or in D = 3 dimensions. A simple square grid made of fibers (with D = 2 and Z = 4) is clearly unstable with respect to shear when the nodes can rotate freely. In cases where a free rotation of the nodes is not possible, the shear stability of the simple square grid is limited by the bending moments, which the nodes and struts can withstand.

However, cellular structures are usually much stronger when the struts are loaded in tension rather than in bending. Hence, structures fulfilling inequality, where any type of loading will result in tension and compression of the fibers only, are likely to be stronger. In the Euplectella skeletal system, three main spicular struts (horizontal, vertical, and one of the two possible diagonals) are joined in every node of the square grid, which means that Z = 6. This is just sufficient to fulfill the equation for a two-dimensional grid. Most remarkably, every second square in the skeletal lattice is left without a diagonal fiber. By adding the crossbeams in these empty squares, the number Z would jump to 8, which would be an overdesign in terms of the equation, with no apparent structural advantages for the prevention of shear stresses.

Proposed scheme summarizing the seven levels of structural hierarchy in the skeletal systemof Euplectella sp. (A) Consolidated silica nanoparticles deposited around a preformed organic axial filament (shown on the right).

Proposed scheme summarizing the seven levels of structural hierarchy in the skeletal systemof Euplectella sp. (B) Lamellar structure of spicule made of alternating organic and silica layers. Inset depicts the organically glued interlayer region.

© Bundling of spicules. (D) (Right) Vertical and horizontal ordering of bundled spicules forming a square-lattice cylindrical cage with every second cell reinforced by diagonal elements (see Eq. 2). (Left) The node structure. Bundling of spicules.

Hierarchical levels , A to D, describe the structure of the Euplectella skeletal system at its early stages of development the “ flexible phase” . During maturation, the flexible cage is rigidified into a Bstiff sponge as a result of the use of two additional levels of structural hierarchy.

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(E) Cementation of nodes and spicules in the skeletal lattice with layered silica matrix. (Inset) Fiber-reinforced composite of an individual beam in the strut. (F) Surface ridges protect against ovalization of the skeleton tube. (G) Flexural anchoring of the rigid cage into the soft sediments of the sea floor.

All the fibers become joined at the nodes of the square grid with silica cement that effectively coats the entire skeletal lattice and thus forms the matrix of a ceramic fiber composite. The only exception is the region where basalia (anchor spicules) emerge from the base of the composite structure. It is also noteworthy that the cement itself exhibits a laminated architecture that hinders crack propagation through this silica matrix.

The resultant rigid structure ensures that the sheet

Material organization in nature - Advanced Sustainability

forming the cylinder is very stable in two dimensions with a number of measures to reduce the intrinsic brittleness of glass. Finally, the cylindrical cage must also be stable in three dimensions, and the main limitation is the ovalization of the cylinder, which reduces the bending stability of the tubelike cage.

In this sense, it is very likely that the helical ridges around the skeleton of Euplectella sp. , in conjunction with the consolidating silica matrix discussed above, serve primarily a mechanical function in preventing ovalization of the sponge skeleton. This argument is further supported by the fact that the ridges are absent in the narrow bottom portion of the tube.

(A) SEM of a fractured laminated spicule.

To ensure the stability of the tube with the vertically growing diameter, there is a distinct increase of the surface density and thickness of the external ridges in the upper regions of the skeletal system.

Exposed to currents, the elevated rigid sponge cage attached to the ocean floor will experience bending stresses that are concentrated at the anchor point. Two mechanical strategies may counteract the stress concentration: to stiffen the anchor point, which will withstand bending forces up to a certain limit and then break, or to make the anchor very flexible. The sponge uses the latter strategy by loosely incorporating the basalia (anchor) spicules into the vertical struts of the

(B) Examination of a polished cross section of the spicule from a related species clearly reveals crack deviation by the organic layers. Scale bars for both micrographs, 10 mm.

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rigid cage. The advantage of this strategy is that there is no limiting stress from currents, and the cage swings freely in the ocean because of the inherent flexibility of the individual spicules that form the connection.

The structural complexity of the glass skeleton in the sponge Euplectella sp. is an example of nature’ s ability to improve inherently poor building materials. The exceptional mechanical stability of the skeleton arises from the successive hierarchical assembly of the constituent glass from the nanometer to the macroscopic scale. The resultant structure might be regarded as a textbook example in mechanical engineering, because the seven hierarchical levels in the sponge skeleton represent major fundamental construction strategies such as laminated structures, fiber reinforced composites, bundled beams, and diagonally reinforced square-grid cells, to name a few. We conclude that the Euplectella sp. skeletal system is designed to provide structural stability at minimum cost, a common theme in biological systems where critical resources are often limited. We believe that the study of the structural complexity of unique biological materials and the underlying mechanisms of their synthesis will help us understand how organisms evolved their sophisticated structures for survival and adaptation and ultimately will offer new materials concepts and design solutions.

Case II - Self-cleaning hydrophobic surface of the Sacred lotus

Material organization in nature - Advanced Sustainability

Introduction Nature offers a variety of surfaces, which exhibit evolutionarily optimized functional properties. In recent years, Biomimetics - an approach that involves the transformation of the underlying principles discovered in nature into man-made teclmology in gaining popularity in newly emerging fields such as micro/nano-electronics to structural engineering. As an example, the unique ability of Lotus leaf surface to avoid getting wet by the surrounding water, popularly known as the "Lotus effect" has motivated scientists world wide to modify/fabricate surfaces for creating artificial superhydro-phobic surfaces .

Superhydrophobic surfaces have also been created by the direct replication of Lotus leaf using the process of nanocasting. Motivated by the surface topography of Lotus leaf, tribologists have modified/fabricated surfaces by means of ionbeam roughening of polymeric surfaces and fabrication of bio-mimetic nano-patterns in order to enhance the tribological performance at micro/nano-scales through the reduction of contact area. These investigations were directed towards enhancing the tribological performance of elements of microelectromechanical systems (MEMS), which are small in size and operate at nano/micro-scales. At these scales of operation, the large surface-to-volume ratio results in high

surface forces such as adhesion and friction, which decrease the performance of MEMS devices. In this paper, we report on a simple biomimetic approach to obtain enhanced microtribological property, which involves the direct replication of natural leaves of waterrepellent plants using a capillarity-directed soft lithographic technique.

In several Asian religions the Lotus flower: Nelumbo Nucifera; is revered as the symbol of purity. The basis of this consideration is based on the self-cleansing property of the leaves of the Lotus flower: even when emerging from muddy waters the leaves unfold untouched by the pollution.

This property of self-cleansing has been researched thoroughly and is ascribed to the interaction between the surface of the Lotusleaves and the water, resulting in high waterrepellency of the surface. This discovery of the Lotus-effect is of great technological interest. By transferring this effect to artificial surfaces, yielding surfaces that can be cleaned by a simple rainfall, numeral technical applications are possible.

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The Lotus effect In order to describe the background of the Lotuseffect, an exact definition is in order: a surface which shows the Lotus-effect is superhydrophobic, expressed by a contact angle larger than 150Âş. Due to this superhydrophobicity, water tends to roll off the surface, even if the surface is tilted slightly, and cleans the surface of a contamination in its way.

A droplet takes up the dust covering a lotus leaf

How does a lotus leaf acquire this superhydrophobicity? Starting from the late 1970’ s, scanning electron microscopic studies on biological surfaces have revealed a large micro structural diversity. A lot of plants showed a combination of microstructure and nanostructure on their surface which minimizes the contact area with anything that came into contact with the surface. The leaves of a lotus plant showed epidermal cells on its rough surface covered with

Material organization in nature - Advanced Sustainability

wax crystals.

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drop, forming a spherical droplet.

Contaminations on the surface are usually larger than the cellular structure of the leaves, leaving the particle resting on the tips of the latter. As the result, the contact area and thus the interfacial interaction is minimized. When a water droplet rolls over the contamination, energy through absorption is gained, even is the particle is hydrophobic.

SEM-image of lotus leaf. The micro structural epidermal cells are covered with nanoscopic wax crystals. Bar: 20 Âľm.

The particle is then removed from the surface if the energy gained by absorption to the water droplet is larger than the energy it costs to remove the particle from the leaves, which is usually the case due to the small contact area.

The Lotus-effect: contaminating particles adhere to the droplet and are removed when the droplet rolls off the surface. Bar: 50 Âľ m.

A water droplet on a lotus leaf.

The wax crystals provide a water-repellent layer, which is enhanced by the surface roughness according to the models of Wenzel and Cassie.

The wax crystals are badly wettable. As a result of this, water droplets on the surface tend to minimize the contact between the surface and the

Diagram showing the cleaning process of a rought surface.

Contaminating particle on a regularly sculptured wing surface of Cicada orni (a plant with a surface structure similar of that of a lotus plant), demonstrating the decreased contact area between a particle and a rough surface. Bar:1 Âľm

Material organization in nature - Advanced Sustainability

Physical basis of the Lotus-effect Foundations: There are different forces acting upon a liquid drop on a surface. Following simple goniometric rules, Young3 θderived that the contact angle θY, from here onwards called Young’ s angle, is given by the relation [1]: cos θY = YSV - YSL YLV where Yij denotes the surface tension (energy per unit surface) of the interface ij and where s, l and v designate the solid, liquid and vapor phase. The equation can also be derived from an energy consideration. The surface energy E can be given by equation [2]: E = A lv Y lv+ A sl Y sl+ (A s- A sl ) Y sv [2] , in which Aij is the surface area between the phases i and j, and As is the total surface of the solid.

Several remarks can be made about Young’ s equation: 1. Forces acting in the vertical direction are not taken into consideration. Since the surface tension exerts all along the liquid/vapor contact, there must also be an opposing force acting on the

solid, which the solid resist because of its elasticity. Roughly, Hooke’ s law indicates that deformation should be in the order γlv/E where E is the Young’ s modulus of the solid. For hard solids, this deformation is hardly observable. However, for soft solids like gels an obvious deformation can be seen.

2. Recent research by T. Pompe et al4 has shown that for tiny drops, the contact line tension τ (excess free energy of a solid-liquid-vapor-system per unit length of the contact line) should be taken into consideration. A characteristic length scale for the influence of τ can be calculated by relating a typical value of τ to a typical value of γ, which yields τ/γ = 10-11 J m-1 / 10-2 J m-2 = 1 nm.

Thus for droplets smaller than 1 μm, a measurable influence can be expected from the contact line tension and an angle correction should be made in the order of τκ/γ, where κ is the curvature of the contact line.

3. While surface tensions in a large range have been measured, varying between 20 mN/m to 1000 mN/m, there is no rule stating that the ration γsv-γsl / γlv has to be smaller than unity. Two cases seem to be of particular interest: (A) If γsvγsl is larger than γlv, the drop tends to spread completely over the solid, resulting in a situation of complete wetting (θ = 0°) (B) If γsv-γsl is a lot smaller than γlv, the drop should be sitting on the

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solid like a marble (θ = 180°). However, no physical systems have been reported which realizes such a situation. For example, water on highly hydrophobic smooth surfaces make contact angles in the order 120°.

4. Young’ s equation assumes the solid surfaces to be perfectly smooth and chemically homogenous.

Material organization in nature - Advanced Sustainability

Rough surfaces Wetting in reality is more complex than described above. This is mainly due to the non-ideality of the surface, which can be both rough and chemically heterogeneous. While the latter can be accounted for by considering a locally different compound with different properties (and thus a different surface tension), the former can’ t be corrected this easily. The earliest work on the effect of surface roughness on contact angles can be attributed to Wenzel and Cassie and Baxter.

They provided different expressions for apparent contact angles, based on different average characteristics of a rough surface Wenzel assumed the liquid fills up the grooves in on a rough surface and stated that on a rough surface for an identically same increase in the free liquid area at the upper surface of the drop (i.e. the liquidvapor-surface), a greater amount of actual surface is wetted under it than compared to a smooth area.

Thus, the net energy decrease on wetting a waterrepelling surface will be greater for the rougher surface than a smooth surface and thereby enhances its water-repellency. The same analogy goes for water-attracting surfaces, thus making them more water attracting.

Therefore, according to Wenzel, a distinction must be made between the total (or actual) surface and the superficial (or geometric) surface.

.In the approach of Cassie and Baxter it is assumed that the liquid forms a composite surface on the rough substrate, the liquid does not fill the grooves on the rough surface. In this case, the liquid-surface interface is actually an interface consisting of two phases, namely a liquid-solid inter face and a liquid-vapor inter face.

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Measurements on the hysteresis of the contact angle have been done by Johnson and Dettre. Data reported on the advancing contact angle θa and the receding contact angle θr on surfaces of wax with variable roughness.

Hysteresis of the contact angle Another complexing factor is commonly called the hysteresis of the contact angle, i.e. different contact angles can coexist along the contact line.

This can be observed rather easily: small drops of liquid can remain immobile on a tilted surface (like smaller rain drops on a vertical window). These droplets have a smaller angle at the back of the drop (at the receding end, with contact angle θr), and a larger angle on the front of the drop (at the advancing end, with contact angle θa), generating a capillary force to balance the weight of the drop.

This hysteresis, commonly denoted Δθ, can be the result of different effects.

Firstly, it can be the effect of chemically heterogeneity of the surface: consider a surface on which the contact angle is θ1 on one end and θ2 on the other end, the contact angle will vary between these two extremes on the contact line.

The same reasoning applies to a discontinuity of the surface roughness, leading to different angles

Of interest is the effect of the surface roughness on the hysteresis. As the roughness (here defined only qualitively), increases, we first notice a large increase in hysteresis, although the variations of the angles themselves are relatively small.

Then, as the roughness increases further, the hysteresis nearly vanishes due to the large increases in the contact angles. Thus, increasing surface roughness not only enhances the

Material organization in nature - Advanced Sustainability

hydrophobicity of a hydrophobic surface, as predicted by the Wenzel model and the CassieBaxter-model, but also has a large effect on the contact angle hysteresis.

Contact angle measurements Different approaches can be used for measuring contact angles of nonporous solids, a goniometric approach and a tensiometric approach, with both having their advantages and their drawbacks.

Another approach is used when measuring the angles of porous substrates, involving the use of a tensiometer and the Washburn method. These three approaches shall be described briefly in the following sections.

. evaporation of by removal of the liquid directly.

The large advantage of goniometry comes from its relative simplicity. It can used for almost any solid, as long as it has a relatively flat portion or a regular curvature and can be fitted on the stage of the instrument.

The main disadvantage of the goniometric approach is the subjectivity of the researcher in assigning the tangent line. This problem can be reduced by computer analysis of the droplet shape. The requirement of a surface large enough a hold a droplet is another problem, yielding the goniometric approach a very poor technique for measurements on fibers.

Tensiometry

Goniometry The basis for the goniometric approach is the analysis of the shape of the drop. The contact angle can be found directly by measuring the angle formed between the solid and the tangent of the drop of an image made of the drop. A typical goniometric instrument consists of a light source, sample stage, lens and image capture. Hysteresis can also be measured using the goniometric approach: the advancing contact angle is measured by slowly adding liquid to the drop, while the receding contact angle can be measured by slowly removing liquid from the drop, either by

The tensiometric method measures the forces that are present when a sample of solid is brought into contact with a test liquid. The contact angle can than be calculated when the forces of interaction, the surface tension and the geometry of the solid is known. Firstly, the surface tension of the liquid is measured, usually with either a Wilhelmy plate or a DuNouy ring. Then, a sample of the solid to be tested is hung to a balance above the liquid. When the liquid is raised it comes in contact with the solid and a different force is detected on the balance. The point at which the solid contacts the liquid is called the zero depth of immersion. If the

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solid is put deeper into the liquid, the detected force is a sum of the wetting force, the weight of the probe and the buoyancy. The weight of the probe can be measured beforehand and set to zero, while the effect of the buoyancy can be removed by extrapolating the force back to the zero depth of immersion, leaving the resulting wetting force.

This wetting force is defined as the product of the surface tension between the liquid and the vapor, the perimeter of the probe and the cosine of the contact angle. The contact angle obtained from this calculation is the advancing contact angle θa when the solid is immersed in the liquid, and the receding contact angle θr when the solid is retracted from the liquid. Static contact angles can be estimated by reducing the rate of immersion or retraction.

There are many advantages of the tensiometric approach over the conventional goniometric method. Hysteresis can be easily measured easily.

Contact angles on fibers, which posed a problem for the goniometric approach, can be measured with the tensiometric approach. Coatings can also be measured by coating a simple solid substrate before measuring. One final advantage is the measurement is down around the entire perimeter of the immersed solid, giving an averaged value for the contact angle.

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Tensiometric measurements also have two large constraints. Firstly, the enough liquid must be available to immerse the solid in. Secondly, there are several requirements for the solid sample. It must be formed in such geometry so it has a constant perimeter over a portion of its length. It must also have the same surface on each side that contacts the liquid and be small enough to be hung to the balance of the tensiometer.

Washburn method The wetting of powder and porous structures is difficult to measure due to the complication of trapping liquid in this the pores. A method for solving this has been developed by Washburn: if a porous solid is put into contact with a liquid, liquid will rise in the pores. ,

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