Material Organization in nature

Material organization in nature

Biotechnology materials

Biomimetics

B i o m i m e t i c s r e f e r s t o h u m a n - m a d eprocesses,substances, devices, or systems thatimitate nature, and has led to the development ofnew biologically inspired materials based onbiological analogs. The research in this area caneither be focused on the investigation of naturalmaterials, or on the processes that optimize thestructure of materials in a manner similar to thatoccurring in nature. Therefore, biology canbecome the basis for developing new processesrequired for synthesizing materials, whilemechanics can be used to interpret the manner inwhich the properties and functionality associatedwith the structure of natural materials haveenabled them to adapt to environmental stimuli.

Each process is examined for mechanisms, scaleof effect, and opportunity for creative humanintervention or utilization.

Learning from and mastering Nature's conceptsnot only satisfies humankind's insatiable curiosityfor understanding the world around us, but alsopromises to drive a paradigm shift in modernmaterials science and technology.

The Role of Mechanics in Biological andBiologically Inspired Materials

In the development of new materials, researchershave recently turned to nature for inspiration andassistance. A special emphasis has been placedon understanding the development of biologicalmaterials from the traditional correlation ofstructure to property, as well as correlatingstructure to functionality. The natural evolution ofstructure in biological materials is guided by theinteraction between these materials and theirenvironment. What is most notable about naturalmaterials is the way in which the structure is ableto adapt at a wide range of length scales. Much ofthe interaction that biological materials experienceoccurs through mechanical contact. Therefore, todevelop biologically inspired materials it isnecessary to quantify the mechanical behavior ofand mechanical influences on biologicalstructures with the intention of defining the naturalstructureproperty- functionality relationship forthese materials.

Near the end of the twentieth century, a new focuswas p laced on micro techno logy andnanotechnology. This was predicated on newcharacterization technologies, such as atomicforce microscopy, that enabled visualization ofnatural phenomena down to the atomistic scale,as well as microtensile testers and nanoindenters

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for microscale and nanoscale mechanicalcharacterization. At these size scales, new naturalphenomena were revealed that presentedscientists and engineers with a novel approach toengineering materials and structures.

For the most part, the science and engineering ofsynthetic materials have been separated intoclasses of structures, length scales andfunctionality that are used to differentiatedisciplines such as experimental mechanics andmaterials science from each other. However,biological materials do not conform to disciplinaryboundaries, since they possess structures thatspan across a full range of length scales in order toreact to a variety of environmental stimuli withoptimal functionality. A number of technologicalbreakthroughs may be achieved through mimicryof the multi-scale optimization of structure andfunctionality in natural materials, such as materialsystems with morphogenesis capabiiities andbimorphic explorer robots with versatile mobility.

The translation of this multi-scale optimization ofstructure and functionality to the science ofadvanced materials is a part of the new field wherescience and engineering are joined together:biomimetics.

Material organization in nature - Advanced Sustainability

Fibrous Tissues

One of the most ubiquitous of biological materialsis fibrous tissue, which is an aggregate of cellscharacterized by a helical fibrous structure. Themechanics of fibrous tissues has become ofinterest recently because the peculiar mechanicalcharacteristics of tissues within an organism aretailored to their specific functional needs, both bythe properties of the constituent "building blocks"and their structural organization.Thus, they tend to have a hierarchical structureand very often they have helical fibers in one ormore levels within their hierarchy.

Although there is a huge range of biologicalfibrous structures, all come from a small numberof building blocks in terms of fibers and matrixmaterials (or ground substances). The mainfibrous building blocks are broadly polypeptides inmammalian structures (e.g., collagen and elastin)and polysaccharides in plant structures andinsects (e.g., chitin and cellulose). The matrixmaterials are globular proteins or glycoproteinsand water in uncalcified soft tissues. In hardtissues, hydroxyapitite and lignin are the mostcommon matrix/filler materials. The smallvariation in the basic components of biologicalmaterials implies that the large variations inobserved properties are the direct result ofstructural variations.

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Mechanics of helical structures

Helical fibers can be tailored to suit the mechanicalenvironment by nature of relative fiber movementscaused by realignment of fibers within the helix.These movements can be controlled by the inter-fiber force, which is related to the helix angle, andthe nature of solid or viscous friction between thefibers, or by the shear modulus of a solid matrix.

This leads to a very versatile range of mechanicalproperties governing flexibility, damage tolerance,energy absorption, and linear force-pressureactuation that are dictated by the nature of theinter-fiber forces. Inter-fiber forces arise becausethe asymmetrical nature of a helix it will tend to tryand unwind and straighten out when loaded alongits long axis. Often practical constraints existwhich prevent the helix from unwinding. Forexample, other helical fibers may be wound in thesame and opposite direction. In this case, forceswill develop between different fibers that are afunction of the geometry and can be givenapproximately with simple formulae.

There is a great deal of interest in developing morecomplex mechanical models that can take intoaccount additional factors, such as geometricalchanges during loading, bending, twisting andfrictional effects.The geometry of helical structures also results in a

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

The nature of the fiber bundle gives rise to anotheradvantage in terms of damage tolerance: crackisolation. Given a sufficiently weak interfacebetween fibers, a crack will not pass from one fiberto the next. Additionally, because of lateral forcesbe tween f ibe rs caused by the he l i xstructurepulling itself together in tension, a breakin the fiber will gradually take up the load until atsome distance from the break it regains its fullshare of the load. In contrast to a simple actually aforce between the fibers this mechanism willoccur even if the interface between the fibers is aviscous fluid or nothing (i.e., relying on inter-fiberfrictional forces).

Fibrous bundles are also capable of absorbingtremendous amounts of energy. Using the inter-fiber shear mechanism, a tensile structure can bedesigned with significant levels of hysteresiswithin a load cycle, which may be time-dependentviscoelastic behavior (in the case of a viscous fluidinterface) or time-independent Coulomb-typedamping (for a frictional interface).


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

Fracture toughness might gradually become lessimportant in another area where greater strengthwould be required. Springs or mounting pointscould be integrated into a single part by simplyadapting the modulus. In the case of a compositematerial, this type of design could be implementedby orienting the polymer chains or crystallinity inthe matrix structures, as well as by varying thepercentage of reinforcement.

To fully implement the biomimicry of wood,thematerial would have to adapt to the application.So, if a system encountered unexpected loading inuse, the material would adapt to the new loadingby emphasizing the need for increased strength ormodulus. The environment would trigger activecontrol and dynamic repair. The biological worldcan provide inspiration and direction fordeveloping this type of integrated system andmaterial design. Additionally, the design processcan mimic the genetic adaptation to environmentaldemands for the development of shape andmaterials for a particular application. Furthermore,it is notable that wood serves not only as astructural material for the tree.

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Examples in Nature

Wood is another ubiquitous biological material thatrepresents adaptation of a plant species to exploitan ecological niche through a multi-scalestructure. Wood makes use of a variety of helicalstructures to create a structure that has bothstiffness and strength adapted to ecological needsand represents a genetic adaptation to thesuccess of a particular competitive strategy forgrowth.

For example, early in the life of the tree the woodemphasizes the need to grow quickly and competefor light. Later in life, wind and other environmentalloads pose the greatest risk to the tree. Themature wood that is produced is thereforestronger, but less height results from the energyinvestment. Both the molecular structure and thephysical orientation of the structural elementsadapt, as a result of the changing needs duringgrowth.

The engineering equivalent of this approach wouldrequire that not only the shape of a component bedesigned for an application, but the structure of thematerial at the microscopic and the molecular levelwould adapt for each application as well. Theengineering equivalent to adaptation during the lifewould be in-service changes in the material.So, for example, if the structure of an engineered Multi-scale structure of wood

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

R


Case I - Material organization of the Euplectella marine sponge

Hierarchically assembled fibrous material

Nature fascinates scientists and engineers withnumerous examples of exceptionally strongbuilding materials. These materials often showcomplex hierarchical organization from thenanometer to the macroscopic scale. Everystructural level contributes to the mechanicalstability and toughness of the resulting design.

For instance, the subtle interplay between thelattice structure, fibril structure, and cellulose isresponsible for the remarkable properties ofwood. In particular,it consists of parallel hollowtubes, the wood cells, which are reinforced bynanometer thick cellulose fibrils wound helicallyaround the cell to adjust the material as needed

Deformation occurs by shearing of a matrix rich inhemicelluloses and lignin, “ gluing” neighboringfibrils, and allowing a stick-slip movement of thefibrils. Wood is an example that shows the widerange of mechanical performance achievable byconstructing with fibers.

Bone is another example of a hierarchicallyassembled fibrous material. Its strength criticallydepends on the interplay between differentstructural levels— from the molecular/nanoscaleinteraction between crystallites of calciumphosphate and an organic framework, through the

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

Whereas wood is fully organic material, bone is acomposite, with about half organic and halfmineral components tightly interconnected at thenanoscale. However, nature has also evolvedalmost pure mineral structures, which - despitethe inherent brittleness of most minerals- aretough enough to serve as protection for theorganism.

In mollusk nacre, for example, the tougheningeffect is due to well-defined nanolayers oforganics at the interfaces between microtablets ofcalcium carbonate. In such structures, the stiffcomponents (usually mineral) absorb the bulk ofthe externally applied loads. The organic layers, inturn, provide toughness, prevent the spread of thecracks into the interior of the structure, and evenconfer a remarkable capacity for recovery afterdeformation (13).

Glass is widely used as a building material in thebiological world, despite its fragility. Organismshave evolved means to effectively reinforce thisinherently brittle material. It has been shown thatspicules in siliceous sponges exhibit exceptionalflexibility and toughness compared with brittlesynthetic glass rods of similar length scales. The

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Spicules in siliceous sponges

mechanical protection of diatom cells wassuggested to arise from the increased strength oftheir silica frustules.

The Eup l ec t e l l a sp . i s a deep -sea ,sedimentdwelling sponge from the WesternPacific.

Sponges are now among the central artifacts in anemerging branch of science: biomimetics. That'sthe study of whatever nature does well - and howthat may inspire better tools, materials, andprocesses. Harvard physical chemist JoannaAizenberg is particularly interested in how livingorganisms form robust and elegant inorganicstructures. The glass fibers framing those deep-sea sponges, for instance, are stronger and moreoptically efficient than anything humankind can yetmake.

Structural properties of biosilica were observed inthe hexactinellid sponge Euplectella sp.Consolidated, nanometer-scaled silica spheresare arranged in well-defined microscopicconcentric rings glued together by organic matrixto 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 of the Euplectella sp.


cylindrical square-lattice cagelike structurereinforced by diagonal ridges.

The ensuing design overcomes the brittleness ofits constituent material, glass, and showsoutstanding mechanical rigidity and stability. Theglass fibers framing those deep-sea sponges, forinstance, are stronger and more optically efficientthan anything humankind can yet make.

The individual spicules are, however, just onestructural level in a highly sophisticated, nearlypurely mineral skeleton of this siliceous sponge.

The assembly of a macroscopic, mechanicallyresistant cylindrical glass cage is possible in amodular, bottom-up fashion comprising at leastseven hierarchical levels, all contributing tomechanical performance. These include silicananospheres that are arranged into concentriclayers separated from one another by alternatingorganic layers to yield lamellar fibers.

The fibers are in turn bundled and organized withina silica matrix to produce flexurally rigid compositebeams at the micron scale. The macroscopicarrangement of these beams in a rectangularlattice with ancillary crossbeams is ideal forresisting tensile and shearing stresses.

Finally, we identify various structural motifs that

Material organization in nature - Advanced Sustainability7

provide additional structural benefits to thisunique glass skeletal system.

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) withlateral (“ oscular” ) openings (1 to 3 mm indiameter). The diameter of the cylinder and thesize of the oscular openings gradually increasefrom the bottom to the top of the structure. Thebasal segment of Euplectella sp. is anchored intothe soft sediments of the sea floor and is looselyconnected to the rigid cage structure, which isexposed to ocean currents and supports the livingportion of the sponge responsible for filtering andmetabolite trapping (23, 24). The characteristicsizes and construction mechanisms of theEuplectella sp. skeletal system are expected to befine-tuned for these functions.

At the macroscale, the cylindrical structure isreinforced by external ridges that extendperpendicular to the surface of the cylinder andspiral the cage at an angle of 45. The pitch of theexternal ridges decreases from the basal to the topportion of the cage. The surface of the cylinderconsists of a regular square lattice composed of aseries of cemented vertical and horizontal struts,each consisting of bundled spicules alignedparallel to one another, with diagonal elementspositioned in every second square cell.

point load is applied to the surface, one mayexpect that the damage will be restricted to theoutermost layers. A larger number of individualglass layers should protect the spicule moreeffectively from this type of damage. Thin organicinterlayers seem also to be important to preventcracks from propagating to inner layers under theinfluence of indentation. The observed decrease ofthe silica layer thickness from the spicule core tothe periphery is likely to provide an additionalreinforcement to the spicules. Thicker inner layershelp enhance mechanical rigidity of the spicule,whereas the thinner outer layers effectively limitthe depth of crack penetration.In a further level ofhierarchy, spicules are joined into parallel bundles,a well-known construction principle in ceramicmaterials. Generally, a bundle of fibers with slightlydifferent strength will have a much larger defecttolerance (and, therefore, strength) than each ofthe individual fibers.

Indeed, if one fiber fails (e.g., under tension),neighboring ones still hold, and the crack in thefirst fiber will be deflected at the interface to itsneighbors (or at the interface between the fiberand cement). A weak lateral bonding betweenfibers (or between fiber and matrix) is essential forthis toughening mechanism to work.The bundledspicules are arranged horizontally and verticallyinto a square-grid cylindrical cage reinforced byancillary diagonal fibers running in both directions.

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These layers are arranged in a cylindrical fashionaround a central proteinaceous filament and areseparated from one another by organic interlayers.Etching of spicule layers and the surroundingcement showed that at the nanoscale thefundamental construction unit consists ofconsolidated hydrated silica nanoparticles (50 to200 nm in diameter). The different levels ofstructural complexity are schematically shown in.In the following discussion, each hierarchical levelis examined from the mechanical perspective.

The first level is biologically produced glasscomposed of consolidated silica nanospheresformed around a protein filament. Glass as abuilding material suffers primarily from itsbrittleness. This means that its strength is limitedmostly by surface defects where the appliedstresses concentrate.

A scratch in the surface of glass readily inducesfracture. If we consider that surface defects in thebiosilica may be induced by external point loads,either biologically or otherwise applied, ascratched plain glass spicule would lose most ofits strength and would fracture when subsequentlyloaded in tension or bending.The intrinsically lowstrength of the glass is balanced at the nextstructural level. The spicule as a whole can beregarded as a laminated composite in which theorganic interlayers act as crack stoppers. If a

Scanning electron micrographshowing that each strut is composed ofbundled multiple spicules (the arrowindicates the long axis of the skeletallattice). Scale bar, 100 mm.


Fragment of the cage structure showingthe square-grid lattice of vertical andhorizontal struts with diagonalelements arranged in a chessboardmanner.

E) SEM of the HF-etched (25) junctionarea showing that the lattice is cementedwith laminated silica layers. Scale bar, 25mm. (F) Contrast-enhanced SEM imageof a cross section through one of thespicular struts, revealing that they arecomposed of a wide range of different-sized spicules surrounded by a laminatedsilica matrix. Scale bar, 10 mm.

Theoretical analyses of strut structures haveshown that when the number of struts per node, Z,exceeds a certain value, the structure is stableeven if the nodes can rotate freely. Deshpande etal. have given the stability limit as Z ≥ 6 ( D - 1 ) forgrids in D = 2 or in D = 3 dimensions. A simplesquare grid made of fibers (with D = 2 and Z = 4)is clearly unstable with respect to shear when thenodes can rotate freely. In cases where a freerotation of the nodes is not possible, the shearstability of the simple square grid is limited by thebending moments, which the nodes and struts canwithstand.

However, cellular structures are usually muchstronger when the struts are loaded in tensionrather than in bending. Hence, structures fulfillinginequality, where any type of loading will result intension and compression of the fibers only, arelikely to be stronger. In the Euplectella skeletalsystem, three main spicular struts (horizontal,vertical, and one of the two possible diagonals)are joined in every node of the square grid, whichmeans that Z = 6. This is just sufficient to fulfill theequation for a two-dimensional grid. Mostremarkably, every second square in the skeletallattice is left without a diagonal fiber. By adding thecrossbeams in these empty squares, the number Zwould jump to 8, which would be an overdesign interms of the equation, with no apparent structuraladvantages for the prevention of shear stresses.

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Proposed scheme summarizing the seven levels of structural hierarchy in theskeletal systemof Euplectella sp. (A) Consolidated silica nanoparticlesdeposited around a preformed organic axial filament (shown on the right).Proposed scheme summarizing the seven levels of structural hierarchy in theskeletal systemof Euplectella sp. (B) Lamellar structure of spicule made ofalternating organic and silica layers. Inset depicts the organically glued interlayerregion.

© Bundling of spicules. (D) (Right) Vertical and horizontal ordering of bundled

spicules forming a square-lattice cylindrical cage with every second cellreinforced by diagonal elements (see Eq. 2). (Left) The node structure. Bundlingof spicules.

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

Hierarchical levels , A to D, describe the structure ofthe Euplectella skeletal system at its early stages ofdevelopment the “ flexible phase” . Duringmaturation, the flexible cage is rigidified into a Bstiffsponge as a result of the use of two additionallevels of structural hierarchy.

All the fibers become joined at the nodes of thesquare grid with silica cement that effectively coatsthe entire skeletal lattice and thus forms the matrixof a ceramic fiber composite. The only exception isthe region where basalia (anchor spicules) emergefrom the base of the composite structure. It is alsonoteworthy that the cement itself exhibits alaminated architecture that hinders crackpropagation through this silica matrix.The resultant rigid structure ensures that the sheet


forming the cylinder is very stable in twodimensions with a number of measures to reducethe intrinsic brittleness of glass. Finally, thecylindrical cage must also be stable in threedimensions, and the main limitation is theovalization of the cylinder, which reduces thebending stability of the tubelike cage.In this sense, it is very likely that the helical ridgesaround the skeleton of Euplectella sp. , inconjunction with the consolidating silica matrixdiscussed above, serve primarily a mechanicalfunction in preventing ovalization of the spongeskeleton. This argument is further supported bythe fact that the ridges are absent in the narrowbottom portion of the tube.

To ensure the stability of the tube with the verticallygrowing diameter, there is a distinct increase of thesurface density and thickness of the externalridges in the upper regions of the skeletal system.

Exposed to currents, the elevated rigid spongecage attached to the ocean floor will experiencebending stresses that are concentrated at theanchor point. Two mechanical strategies maycounteract the stress concentration: to stiffen theanchor point, which will withstand bending forcesup to a certain limit and then break, or to make theanchor very flexible. The sponge uses the latterstrategy by loosely incorporating the basalia(anchor) spicules into the vertical struts of the

rigid cage. The advantage of this strategy is thatthere is no limiting stress from currents, and thecage swings freely in the ocean because of theinherent flexibility of the individual spicules thatform the connection.The structural complexity of the glass skeleton inthe sponge Euplectella sp. is an example ofnature’ s ability to improve inherently poor buildingmaterials. The exceptional mechanical stability ofthe skeleton arises from the successivehierarchical assembly of the constituent glassfrom the nanometer to the macroscopic scale. Theresultant structure might be regarded as atextbook example in mechanical engineering,because the seven hierarchical levels in thesponge skeleton represent major fundamentalconstruction strategies such as laminatedstructures, fiber reinforced composites, bundledbeams, and diagonally reinforced square-gridcells, to name a few. We conclude that theEuplectella sp. skeletal system is designed toprovide structural stability at minimum cost, acommon theme in biological systems wherecritical resources are often limited. We believe thatthe study of the structural complexity of uniquebiological materials and the underlyingmechanisms of their synthesis will help usunderstand how organisms evolved theirsophisticated structures for survival andadaptation and ultimately will offer new materialsconcepts and design solutions.

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

(A) SEM of a fractured laminated spicule.


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

surface forces such as adhesion and friction,which decrease the performance of MEMSdevices. In this paper, we report on a simplebiomimetic approach to obtain enhanced micro-tribological property, which involves the directreplication of natural leaves of waterrepellentplants using a capillarity-directed soft lithographictechnique.

In several Asian religions the Lotus flower:Nelumbo Nucifera; is revered as the symbol ofpurity. The basis of this consideration is based onthe self-cleansing property of the leaves of theLotus flower: even when emerging from muddywaters the leaves unfold untouched by thepollution.

This proper ty of self-cleansing has beenresearched thoroughly and is ascribed to theinteraction between the surface of the Lotus-leaves and the water, resulting in high water-repellency of the surface. This discovery of theLotus-effect is of great technological interest. Bytransferring this effect to artificial surfaces,yielding surfaces that can be cleaned by a simplerainfall, numeral technical applications arepossible.

13Material organization in nature - Advanced Sustainability

Introduction

Nature offers a variety of surfaces, which exhibitevolutionarily optimized functional properties. Inrecent years, Biomimetics - an approach thatinvolves the transformation of the underlyingprinciples discovered in nature into man-madeteclmology in gaining popularity in newlyemerging fields such as micro/nano-electronics tostructural engineering. As an example, the uniqueability of Lotus leaf surface to avoid getting wet bythe surrounding water, popularly known as the"Lotus effect" has motivated scientists world wideto modify/fabricate surfaces for creating artificialsuperhydro-phobic surfaces.Superhydrophobic surfaces have also beencreated by the direct replication of Lotus leaf usingthe process of nanocasting. Motivated by thesurface topography of Lotus leaf, tribologists havemodified/fabricated surfaces by means of ion-beam roughening of polymeric surfaces andfabrication of bio-mimetic nano-patterns in orderto enhance the tribological performance atmicro/nano-scales through the reduction ofcontact area. These investigations were directedtowards enhancing the tribological performanceof elements of microelectromechanical systems(MEMS), which are small in size and operate atnano/micro-scales. At these scales of operation,the large surface-to-volume ratio results in high

The Lotus effect

In order to describe the background of the Lotus-effect, an exact definition is in order: a surfacew h i c h s h o w s t h e L o t u s - e f f e c t i ssuperhydrophobic, expressed by a contact anglelarger than 150º. Due to this superhydrophobicity,water tends to roll off the surface, even if thesurface is tilted slightly, and cleans the surface of acontamination in its way.

How does a lo tus lea f acqu i re th issuperhydrophobicity? Starting from the late1970’ s, scanning electron microscopic studies onbiological surfaces have revealed a large microstructural diversity. A lot of plants showed acombination of microstructure and nanostructureon their surface which minimizes the contact areawith anything that came into contact with thesurface. The leaves of a lotus plant showedepidermal cells on its rough surface covered with

A droplet takes up the dust covering a lotus leaf

drop, forming a spherical droplet.

Contaminations on the surface are usually largerthan the cellular structure of the leaves, leaving theparticle resting on the tips of the latter. As theresult, the contact area and thus the interfacialinteraction is minimized. When a water dropletrolls over the contamination, energy throughabsorption is gained, even is the particle ishydrophobic.

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

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


wax crystals.

The wax crystals provide a water-repellent layer,which is enhanced by the surface roughnessaccording to the models of Wenzel and Cassie.The wax crystals are badly wettable. As a result ofthis, water droplets on the surface tend tominimize the contact between the surface and the

SEM-image of lotus leaf. The micro structural epidermal cells are covered withnanoscopic wax crystals. Bar: 20 m.µ

A water droplet on a lotus leaf.

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

Diagram showing the cleaning process of a rought surface.

solid, which the solid resist because of itselasticity. Roughly, Hooke’ s law indicates thatdeformation should be in the order lv/E where E isthe Young’ s modulus of the solid. For hard solids,this deformation is hardly observable. However,for soft solids like gels an obvious deformation canbe seen.

γ

2. Recent research by T. Pompe et al4 has shownthat for tiny drops, the contact line tension(excess free energy of a solid-liquid-vapor-systemper unit length of the contact line) should be takeninto consideration. A characteristic length scalefor the influence of can be calculated by relating atypical value of to a typical value of , whichyields / = 10-11 J m-1 / 10-2 J m-2 = 1 nm.Thus for droplets smaller than 1 m, a measurableinfluence can be expected from the contact linetension and an angle correction should be made inthe order of / , where is the curvature of thecontact line.

3. While surface tensions in a large range havebeen measured, varying between 20 mN/m to1000 mN/m, there is no rule stating that the ration

sv- sl / lv has to be smaller than unity. Twocases seem to be of particular interest: (A) If sv-

sl is larger than lv, the drop tends to spreadcompletely over the solid, resulting in a situation ofcomplete wetting ( = 0°) (B) If sv- sl is a lotsmaller than lv, the drop should be sitting on the

τ

τ

τ γ

τ γ

μ

τκ γ κ

γ γ γ

γ

γ γ

θ γ γ

γ


Physical basis of the Lotus-effect

Foundations:

There are different forces acting upon a liquiddrop on a surface. Following simple goniometricrules, Young derived that the contact angle ,from here onwards called Young’ s angle, is givenby the relation :

cos

where Y denotes the surface tension (energy perunit surface) of the interface ij and where s, l and vdesignate the solid, liquid and vapor phase. Theequation can also be derived from an energyconsideration. The surface energy E can be givenby equation [2]:

E = A + A Y + (A - A ) Y [2], in which A is the surface area between thephases i and j, and A is the total surface of thesolid.

Several remarks can be made about Young’ sequation:1. Forces acting in the vertical direction are nottaken into consideration. Since the surface tensionexerts all along the liquid/vapor contact, theremust also be an opposing force acting on the

3

ij

sl s sl sv

ij

s

θ θY

lv

[1]

Y Y

Y

Y

θY = SV - SL

LV

sllv

solid like a marble ( = 180°). However, nophysical systems have been reported whichrealizes such a situation. For example, water onhighly hydrophobic smooth surfaces makecontact angles in the order 120°.

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

θ

.In the approach of Cassie and Baxter it is assumedthat the liquid forms a composite surface on therough substrate, the liquid does not fill thegrooves on the rough surface. In this case, theliquid-surface interface is actually an interfaceconsisting of two phases, namely a liquid-solidinter face and a liquid-vapor inter face.

Another complexing factor is commonly called thehysteresis of the contact angle, i.e. differentcontact angles can coexist along the contact line.This can be observed rather easily: small drops ofliquid can remain immobile on a tilted surface (likesmaller rain drops on a vertical window). Thesedroplets have a smaller angle at the back of thedrop (at the receding end, with contact angle r),and a larger angle on the front of the drop (at theadvancing end, with contact angle a), generatinga capillary force to balance the weight of the drop.

This hysteresis, commonly denoted , can bethe result of different effects.Firstly, it can be the effect of chemicallyheterogeneity of the surface: consider a surfaceon which the contact angle is 1 on one end and

2 on the other end, the contact angle will varybetween these two extremes on the contact line.The same reasoning applies to a discontinuity ofthe surface roughness, leading to different angles

θ

θ

Δθ

θ

θ

Hysteresis of the contact angle


Rough surfaces

Wetting in reality is more complex than describedabove. This is mainly due to the non-ideality of thesurface, which can be both rough and chemicallyheterogeneous. While the latter can be accountedfor by considering a locally different compoundwith different properties (and thus a differentsurface tension), the former can’ t be correctedthis easily. The earliest work on the effect ofsurface roughness on contact angles can beattributed to Wenzel and Cassie and Baxter.They provided different expressions for apparentcontact angles, based on different averagecharacteristics of a rough surface Wenzelassumed the liquid fills up the grooves in on arough surface and stated that on a rough surfacefor an identically same increase in the free liquidarea at the upper surface of the drop (i.e. the liquid-vapor-surface), a greater amount of actual surfaceis wetted under it than compared to a smooth area.Thus, the net energy decrease on wetting a water-repelling surface will be greater for the roughersurface than a smooth surface and therebyenhances its water-repellency. The same analogygoes for water-attracting surfaces, thus makingthem more water attracting.Therefore, according to Wenzel, a distinction mustbe made between the total (or actual) surface andthe superficial (or geometric) surface.

Measurements on the hysteresis of the contactangle have been done by Johnson and Dettre. Datareported on the advancing contact angle a andthe receding contact angle r on surfaces of waxwith variable roughness.

θ

θ

Of interest is the effect of the surface roughness onthe hysteresis. As the roughness (here definedonly qualitively), increases, we first notice a largeincrease in hysteresis, although the variations ofthe angles themselves are relatively small.Then, as the roughness increases further, thehysteresis nearly vanishes due to the largeincreases in the contact angles. Thus, increasingsurface roughness not only enhances the

hydrophobicity of a hydrophobic surface, aspredicted by the Wenzel model and the Cassie-Baxter-model, but also has a large effect on thecontact angle hysteresis.

Different approaches can be used for measuringcontact angles of nonporous solids, a goniometricapproach and a tensiometric approach, with bothhaving their advantages and their drawbacks.Another approach is used when measuring theangles of porous substrates, involving the use of atensiometer and the Washburn method. Thesethree approaches shall be described briefly in thefollowing sections.

The basis for the goniometric approach is theanalysis of the shape of the drop. The contactangle can be found directly by measuring the angleformed between the solid and the tangent of thedrop of an image made of the drop. A typicalgoniometric instrument consists of a light source,sample stage, lens and image capture. Hysteresiscan also be measured using the goniometricapproach: the advancing contact angle ismeasured by slowly adding liquid to the drop,while the receding contact angle can be measuredby slowly removing liquid from the drop, either by

Contact angle measurements

Goniometry


. evaporation of by removal of the liquid directly.The large advantage of goniometry comes from itsrelative simplicity. It can used for almost any solid,as long as it has a relatively flat portion or a regularcurvature and can be fitted on the stage of theinstrument.

The main disadvantage of the goniometricapproach is the subjectivity of the researcher inassigning the tangent line. This problem can bereduced by computer analysis of the dropletshape. The requirement of a surface large enougha hold a droplet is another problem, yielding thegoniometric approach a very poor technique formeasurements on fibers.

The tensiometric method measures the forces thatare present when a sample of solid is brought intocontact with a test liquid. The contact angle canthan be calculated when the forces of interaction,the surface tension and the geometry of the solidis known. Firstly, the surface tension of the liquid ismeasured, usually with either a Wilhelmy plate or aDuNouy ring. Then, a sample of the solid to betested is hung to a balance above the liquid. Whenthe liquid is raised it comes in contact with thesolid and a different force is detected on thebalance. The point at which the solid contacts theliquid is called the zero depth of immersion. If the

Tensiometry

solid is put deeper into the liquid, the detectedforce is a sum of the wetting force, the weight ofthe probe and the buoyancy. The weight of theprobe can be measured beforehand and set tozero, while the effect of the buoyancy can beremoved by extrapolating the force back to thezero depth of immersion, leaving the resultingwetting force.

This wetting force is defined as the product of thesurface tension between the liquid and the vapor,the perimeter of the probe and the cosine of thecontact angle. The contact angle obtained fromthis calculation is the advancing contact angle awhen the solid is immersed in the liquid, and thereceding contact angle r when the solid isretracted from the liquid. Static contact angles canbe estimated by reducing the rate of immersion orretraction.

There are many advantages of the tensiometricapproach over the conventional goniometricmethod. Hysteresis can be easily measured easily.Contact angles on fibers, which posed a problemfor the goniometric approach, can be measuredwith the tensiometric approach. Coatings can alsobe measured by coating a simple solid substratebefore measuring. One final advantage is themeasurement is down around the entire perimeterof the immersed solid, giving an averaged valuefor the contact angle.

θ

θ

Tensiometric measurements also have two largeconstraints. Firstly, the enough liquid must beavailable to immerse the solid in. Secondly, thereare several requirements for the solid sample. Itmust be formed in such geometry so it has aconstant perimeter over a portion of its length. Itmust also have the same surface on each side thatcontacts the liquid and be small enough to be hungto the balance of the tensiometer.

The wetting of powder and porous structures isdifficult to measure due to the complication oftrapping liquid in this the pores. A method forsolving this has been developed by Washburn: if aporous solid is put into contact with a liquid, liquidwill rise in the pores.,

Washburn method


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