Spider Silk Inspired Functional MicrothreadsVasav Sahni, Disha V. Labhasetwar, and Ali Dhinojwala*

Department of Polymer Science, Integrated Bioscience Program, The University of Akron, Akron, Ohio 44325-3909, United States

*S Supporting Information

ABSTRACT: We employ the adhesive web building strategy used by modern orb-weaving spiders toproduce functional microthreads that are similar in structure (beads-on-a-string (BOAS) morphology) andadhesive properties to the capture-silk threads of the spider web. The diameter and spacing of droplets(beads) are controlled by varying the viscosity, velocity, and surface tension of the coating fluid. Using thesefunctional threads, we also describe the behavior of the BOAS morphology during contact (mimicking thecollision of an insect with the web) and during separation (mimicking insect rescue from the web). Ourresults show that the BOAS structure performs better than a cylindrical structure for adhesion, which mayexplain why this morphology is so prevalent in spider webs despite the cost of increasing the visibility of theweb.

■ INTRODUCTIONSpiders display innovative behavioral strategies in conjunctionwith micrometer-size custom-made adhesive silk threads incor-porated into prey capture webs.1 The proteins as well as low-molecular-mass organic and inorganic materials used in thesewebs evolved over millions of years into a class of naturaladhesives with outstanding properties. Multiple types ofadhesives are often used in a single spider web; however,the adhesives used to capture prey have received the mostattention. Silk threads spun by modern orb-weaving spiders tocapture prey consist of a beads-on-a-string (BOAS)2-likemorphology, where the beads of glue are composed of adhesivepolymeric glycoproteins3−5 and low-molecular-weight hygro-scopic compounds.6 The string is composed of a pair of softand highly extensible viscoelastic axial silk fibers.7 The BOASthreads are produced from triads of spigots that lie on theposterior spinnerets of spiders. Each triad is composed of agland that produces an axial silk fiber (flagelliform gland), twoglands that secrete glue (aggregate gland), and their respec-tive spigots. The spigot from the fiber gland is arrangedbetween the spigots of the glue glands such that the glue andfibers are simultaneously extruded8 and glue coats the fiber.The composition of the glue, its physical characteristics, and thespinning conditions of the silk produce an initially cylindricalcoating of the glue on the axial silk, which breaks down into anequally spaced micrometer-sized array of glue droplets due toRayleigh instability. After a period of time, the glue dropletsbecome more viscous and develop elasticity, which becomeimportant in enhancing adhesion.5

Interestingly, even though Rayleigh instability results inreducing the exposed surface area (in the absence of no externalforces that may cause deformation of the droplets) of theadhesive coating, the BOAS structure is prevalent. In addition,the BOAS thread is more visible than the cylindrical threadan undesirable characteristic in a trap. The success of BOASmorphology is also evident through other examples, especiallyby its presence in the gumfoot silk threads9 spun by the

cobweb-weaving spiders, the evolutionary descendents of modernorb-weaving spiders.Here, we employ the strategy utilized by modern orb-weaving

spiders to produce functional microthreads (hereafter referredto as “functional threads”). We also tune the magnitude of func-tionality imparted by varying the velocity, viscosity, and surfacetension of the coating material. In general, higher viscosity andvelocity and lower surface tension of the fluid result in theformation of bigger and farther-spaced droplets. Using thesefunctional threads, we describe the behavior of the BOAS andcylindrical morphologies during contact (mimicking collision ofan insect) and during separation (mimicking insect rescue) andshow that the BOAS structure is better suited than a cylindricalstructure for adhesion, despite higher visibility of the adhesivethread in the web.

■ EXPERIMENTAL SECTIONPreparation of Functional Threads . Nylon fibers (gifted by

Goodyear, Akron, OH) of diameter 30 μm were verticallywithdrawn, at a controlled velocity, from a reservoir filled withpoly(dimethylsiloxane) (PDMS) (equal parts of Sylgard 528A andB provided by Dow Corning). The cylindrical coating of PDMSspontaneously breaks into an array of droplets. The thread is placedin a vacuum oven at 80 °C for 2 h to cure the PDMS. To show theeffect of viscosity on drop dimensions and spacing, un-cross-linkedPDMS of kinematic viscosities 10 cst, 100 cst, and 1000 cst(10−5 m2/sec, 10−4 m2/sec, and 10−3 m2/sec, respectively) were used(Dow Corning).

Measurement of Adhesion Force. Sixteen-millimeter samplesof the cured threads, mounted across the gap of a U-shaped cardboardpiece, were clamped onto the top grip of NanoBionix (Agilent Tech.,formerly MTS) as shown in Figure S1 (Supporting Information). A2 mm-wide clean glass plate was clamped onto the bottom grip. Thethread is pushed onto the glass plate to a force of 20 μN at a rate of

Special Issue: BioinspiredAssemblies and Interfaces

Received: August 22, 2011Revised: December 6, 2011Published: December 7, 2011

Article

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0.1 mm s−1 (displacement-controlled loading), held there for 60 s, andthen pulled away from the substrate at a fixed rate (2 mm/s for Figure 2c,d,and 0.5 mm/s and 2 mm/s for Figure 3, inset), while the force-displacement response is recorded (Figure S2). Force is measuredby the displacement of the actuating transducer in the NanoBionix. Themaximum displacement of the transducer is ±1 mm. The forceregistered just before the thread releases contact with the class plate isrecorded as the adhesion force. Ten samples were tested three timeseach. Values are plotted as mean ± SD from 30 measurements each.Measurement of the Tensile Properties. Independent tensile

tests on the threads were performed, by clamping a thread onto the top andbottom grips of the NanoBionix, to find out the strain energy stored (areaunder the stress−strain curve) when the thread is stretched (Figure S3).The maximum strain to determine the energy stored in the thread wasdetermined from the maximum strain experienced by the thread during theadhesion measurements. These tensile tests were performed at the samestretching rates that the threads experienced during adhesion measure-ments, to account for any viscoelastic effects. Strain energy values weredetermined from testing ten 16-mm long thread samples. The equationused to calculate the contribution of the energy stored in stretching thethread is discussed in the main text.

■ RESULTS AND DISCUSSIONA continuous microfiber (Nylon) is pulled vertically out of areservoir containing PDMS at different velocities. We choosePDMS as the liquid because it has low surface tension, and theeffect of gravity on the droplets is negligible (bond number≪1).Depending on the capillary number, Ca, the cylindrical coatingbreaks down into an array of droplets due to Rayleigh instability.The coated fiber is then cured by heating at 80 °C to stabilizeand immobilize the droplets. Figure 1a,b shows a capture threadspun by Argiope trifasciata and functional threads formed bycoating nylon fiber with PDMS.The adhesion of the fibers can be easily tuned by varying the

capillary number. Upon withdrawing a fiber from the reservoir,the thickness of the entrained cylindrical film, e, for bond

number ≪1 (which is the case here), is given by the followingequations:10

=≪

−∼

⎧⎨⎪⎪

⎩⎪⎪

ed

d

1.34 Ca , Ca 1

1.34 Ca

1 1.34Ca, Ca 1

2/3

2/3

2/3(1)

Here, Ca = ηV/γ and d, η, γ, and V are the radius (of theuncoated fiber), viscosity, surface tension, and velocity of thecoating, respectively. Plateau11 and Rayleigh12 showed thatthe initially cylindrical coating breaks into an array of dropssuch that the wavelength of the array, λ, as well as the radius ofthe sphere, R,13 are both dependent on the thickness of thecylindrical coating e.

λ > π +d e2 ( ) (2)

= λ + −⎡⎣⎢

⎤⎦⎥R d e d

34

(( ) )2 21/3

(3)

In essence, by varying η, γ, or V, one can change Ca.Changing Ca will change the thickness of the coating and hencethe radius of the cylinder, which will determine the wavelengthλ of the array of spheres of radius R. Using this principle, thesize and spacing of the drops on the functional threads weretuned by varying the capillary number. Figure 1c shows theeffect of velocity, V, on the size and the spacing of the drops.The volume of the drop as well as the spacing between thedroplets increases with increasing velocity of the coating. Figure1d shows the effect of viscosity, η, of the coating on the volumeand the wavelength of the droplets. Similar to the velocity,increasing the viscosity also results in higher drop volume andlonger wavelength.

Figure 1. Fabrication and tuning of functional threads. (a,b) Capture spiral thread spun by Argiope trifasciata (scale bar is 30μm) and a threadproduced by withdrawing a nylon thread out of a reservoir filled with PDMS, respectively. (c) Effect of velocity of coating on drop dimensions whennylon threads are coated with PDMS of kinematic viscosity 1000 cst at velocities of 690, 2460, and 9460 μm·s−1 (left to right). (d) Effect of PDMSviscosity on drop dimensions. Nylon threads are coated, at 9460 μm·s−1, with PDMS of kinematic viscosities 10, 100, and 1000 cst (left to right).Capillary number increases from left to right. Scale bars in c and d are 150 and 50 μm, respectively.

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The modern orb-weavers have developed an intriguingstructure for their capture threads, utilizing glue droplets asadhesive beads on a very elastic silk thread. The glue dropletsbehave like viscoelastic solids5 and can withstand largeextension as shown in Figure 2a. The “suspension bridge”14-like structure increases the peeling force and makes the capturethreads very sticky. This was one of the reasons we chose to usePDMS as the fluid to mimic this morphology, as cross-linkedPDMS is elastic and stretchy. Figure 2b shows an opticalimage of the functional thread as it is pulled off the surface.Similar to the capture silk threads produced by spiders, asuspension bridge-like structure is observed in the functionalthread (Figure 2b). The adhesion forces required to peel thefunctional threads are shown in Figure 2c. Higher capillarynumber was accompanied by higher force of adhesion. Inter-estingly, capture silk threads spun by different orb-weavingspiders also show similar behavior: generally, capture threadswith bigger and farther-spaced drops demonstrate higheradhesion.14

It has been shown that the force of adhesion depends on themechanical properties of both the fiber and the glue droplets.5

The contributions from the fiber and the glue can be sepa-rated by using a recently developed energy model.5 The workperformed to pull a thread off a surface is consumed instretching of the axial fiber and the energy required to peel thedroplets from the surface. Figure S1 shows a sketch definingthe variables used in the energy model. The total work on thesystem (WT) is calculated by integrating the product of theforce f(h) times the infinitesimal height change dh from h toh + dh.

∫==

=W f h h( ) d

h

h hT

( 0)

( )f

(4)

The strain energy stored in the thread when it is pulled from itsinitial position until it separates from the surface, Ustrain, is given

by the following equation:

∫= σ ε εε=

ε=εU ( ) dstrain

( 0)

( )f

(5)

σ(ε) is the value of load at displacement ε, as measured fromindependent tensile tests. Here, the assumption is that thelength of thread adhered to the substrate at any time during theadhesion measurement is negligible compared to the totallength of the thread, which is reasonable since the width of thesubstrate (2 mm) is much less than the length of the thread(16 mm). Subtracting eq 5 from eq 4 gives the energy requiredto separate the glue drops from the surface, Uglue. Figure 2dshows the energy of adhesion of the glue drops as a functionof the capillary number. The increase in the energy ofadhesion of the glue drops with increasing capillary number,indicating that the increase in force of adhesion is due to theglue drops and not to the difference in tensile properties ofthe thread. The extent of functionality (adhesiveness in thiscase) imparted to a fiber can thus be easily tuned by varyingthe capillary number.Interestingly, when a newly spun capture silk thread (the glue

coating is still cylindrical) spun by Larinioides cornutus isbrought into contact with a clean glass plate and then separatedfrom it, the force of adhesion measured at separation is around3 times lower than when the glue coating has broken into anarray of droplets (Figure 3, inset). The difference in adhesiveforces can be attributed to higher contact area established bythe glue droplets than the glue cylindrical morphology and thehigher energy dissipated in separating the glue droplets than inseparating the glue cylinder, since peeling glue droplets from asurface will have multiple crack-initiation, crack-propagation,and crack-arrest events, whereas peeling a cylinder will requireonly one of each. Using the functional threads as an example,we studied the effect of these factors (interfacial contact areaestablished and energy dissipation during separation) on the

Figure 2. Testing of functional threads. (a) Suspension bridge formed when a capture silk thread spun by Larinioides cornutus is separated from aglass surface. Interestingly, the functional threads produced by coating Nylon threads with PDMS behave similarly and also exhibit the formation of asuspension bridge-like structure when separated from a substrate (shown in panel b). (c) Adhesion force of a functional thread (PDMS-coated nylonthread) as a function of the capillary number (rate of separation of thread from the substrate = 2 mm·s−1). (d) Effect of capillary number on theadhesion energy of the PDMS drops. The energies were determined using a recently developed energy model.5 The error bars are calculated fromthe error in WT and the UStrain from 30 measurements each.

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adhesion of both morphologies (cylinders and spheres) in anattempt to understand the advantage of the BOAS morphologyon the capture silk threads.15

Considering a linear elastic model, we can calculate thedifferences in contact areas between the BOAS morphologyand the cylindrical coating of similar volume (mimicking insectcapture). For the sake of simplicity, we assume the glue dropsto be spherical. (In reality, the glue drops produced by spidersare paraboloidal.) According to the Johnson−Kendall−Roberts(JKR) theory, the contact radius, a, of the circle formed bypressing a deformable sphere onto a rigid flat surface is givenby16

= + π + π + πaRK

P WR WRP WR( 3 (6 (3 ) ) )3 2(6)

In the JKR model, P is the applied load, R is the radius ofcurvature of the sphere, W is the adhesion energy of the spherewith the substrate, and K is related to the effective elasticmodulus (Eeff, K = 4Eeff/3). In the case of the cylindrical thread,a contact rectangle of length, 2l, and width, 2b, is formed uponpressing a deformable cylinder on a rigid flat surface and isgiven by17

π = + πbS

PKlb

WK

38

61.5

0.5 (7)

Here, S is the radius of the cylinder, and other terms aresimilar to those described in eq 5. Figure 3 compares theinterfacial area, calculated assuming JKR contact, establishedby a cylinder and the eventually formed spheres, with a rigidflat substrate. Since the cylinder breaks into an array ofspheres, the volume of the sphere is equal to the volume ofone wavelength of cylinder. For the same loading force, a

sphere establishes higher contact area than a cylinder ofequal volume (Figure 3). (Details of these calculations aregiven in the Supporting Information.) The glue coatingsproduced by orb-weaving spiders, as well as the cross-linkedPDMS coating on the functional threads, exhibit elasticity,and the elastic model in these calculations is used toillustrate that the sphere geometry (BOAS threads) results inhigher contact area with the substrate.In addition to the higher surface area established by the

array of spheres, the BOAS morphology adopted by spidersalso has a higher force required to separate the array ofspheres from a surface (mimicking insect rescue). The higherseparation force is due to the multiple crack-initiation, crack-propagation, and crack-arrest events as opposed to a singleevent when a cylinder is separated from a surface. Kendall18

has showed that different interfaces between materials of dif-ferent thicknesses have a considerable effect on crack propaga-tion: when a crack meets a thicker material, it experiencestransient retardation, whereas when a crack meets a thinnermaterial, it experiences transient acceleration. Hence, periodicstructures (like spider capture silk and functional threads)substantially increase static interfacial fracture energy througharresting cracks at a thicker interface. Moreover, the dynamicinterfacial fracture energy, i.e., resistance to a moving crack, isalso raised due to fluctuations of crack speed at a number ofperiodically spaced interfaces. Kendall’s analysis on peelingtapes suggests that the spacing and diameter of the glue dropsare important in increasing the peeling force. We illustratedthe importance of this hypothesis by referring to the works ofGhatak and Chaudhury.19 For the sake of simplicity, the arrayof drops can be roughly approximated as a one-dimensionaladhesive film having equi-spaced incisions on it (distancebetween incisions = s). For separating a smooth surface of a

Figure 3. BOAS versus cylindrical morphology. Shows the contact area established on glass by equal volumes of cylinder and the eventually formeddroplets, calculated assuming JKR theory, which is applicable here since the nylon fiber is coated with PDMS (Sylgard 528 A and B), which, aftercross-linking, becomes elastic. The volumes of the cylinders and spheres were calculated using volume conservation on the dimensions of the gluedrops on the capture spiral threads spun by Cyclosa turbinata (circles), Leucauge venusta (squares), Metepeira labyrynthia (upright triangle), Araneuspegnia (inverted triangle), Argiope trifasciata (left triangle), and Araneus Marmoreus (right triangle).12 Filled symbols represent spheres, whereas thecorresponding open symbols represent cylinders. Spheres establish higher contact area than cylinders for the same loading force. Inset compares theadhesion of freshly spun capture threads (the coating is still cylindrical) (hashed bars) versus capture threads in which the coating has BOASstructure (solid bars), at different rates of pull-off (speed at which the thread is separated from the substrate). Glue droplets cause the capturethreads to adhere many times stronger than the cylindrical glue coating.

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finite flexural rigidity D, the stress decay length, κ−1, is givenby19

κ =μ

− ⎛⎝⎜

⎞⎠⎟

Dw12

13 1/6

(8)

Here, D = 0.02 N·m, μ = 1 MPa, and w was taken to equal thewidth of a single glue droplet, while s was taken as the wave-length of the droplets (details in the Supporting Information).For the dimension of the array shown in Figure 3, sκ(a dimensionless parameter defined in ref 17, which describesthe thickness and the wavelength of the array), for the array ofbeads varies from 0.3 to 1.3, while separating a cylinder fromthe same surface would have sκ = ∞. It has been shown thatenergy required to separate the film reduces as sκ increases,19

which implies that the energy required to separate a BOASthread will be higher than that required to separate a cylindricalthread. Higher energy dissipated while separating a BOASthread, together with the higher interfacial surface areaestablished by the BOAS morphology demonstrates that theBOAS structure exhibits higher adhesion than the cylindricalstructure.

■ CONCLUSION

In summary, we have mimicked the strategy used by orb-weaversto develop functional microthreads with excellent adhesiveproperties. By varying the capillary number, the structure andmorphology of the functional threads can be controlled. Thesimplicity and scalability of this method over conventionalmethods used to produce such structurestemplate-basedsynthesis,20 vapor-phase synthesis,21 solution-phase deposition,22

and coaxial electrospinning23allows rapid and easy large-scalefabrication of one-dimensional BOAS structures with a widerange of compatible component materials. The BOAS structureestablishes higher interfacial contact area than a cylindricalmorphology for the same applied load. Also, the energy requiredto separate a BOAS thread is higher on account of multiplecrack-initiation, crack-propagation, and crack-arrest events. Theseresults demonstrate that the BOAS structure has higher adhesionthan a cylindrical morphology, which may explain why the BOASmorphology is seen in multiple species of spider and overevolutionary history.

■ ASSOCIATED CONTENT

*S Supporting InformationDetails of calculations of interfacial contact area, the schematicof the experimental setup, typical force−distance curve duringan adhesion measurement, and a typical tensile test data forBOAS. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: ali4@uakron.edu.

■ ACKNOWLEDGMENTS

This work was supported by the National Science Foundation.We also acknowledge the financial support of the AustenBioinnovation Institute in Akron (ABIA).

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