Adhesion of nonplanar wrinkled surfaces

Adhesion of Nonplanar Wrinkled Surfaces

Santanu Kundu,1y Chelsea S. Davis,1 Thomas Long,1 Ravi Sharma,2 Alfred J. Crosby1

1Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts

2Bausch & Lomb Inc., Rochester, New York

Correspondence to: A. J. Crosby (E-mail: [email protected])

Received 24 September 2010; revised 1 November 2010; accepted 1 November 2010; published online 29 November 2010

DOI: 10.1002/polb.22181

ABSTRACT: Topological patterns on polymer surfaces can sig-

nificantly alter and control adhesion. In this study, the effect of

surface wrinkles on a spherical surface on adhesion has been

studied. Surface wrinkling induced by swelling of a crosslinked

polydimethylsiloxane elastomer constrained by a stiff, thin sur-

face layer (silicate) is used to produce topographic features of

various length scales over a large curved area. By controlling

the properties of the stiff layer and the applied strain condi-

tions, surface wrinkles of varying amplitude and wavelength

are obtained. The effect of wrinkle morphology on adhesion is

quantified, and the results display a transition from enhance-

ment of adhesion to decrease depending upon wrinkle dimen-

sions. A simple phenomenological model is proposed that

describes the change of adhesion behavior as a function of

wrinkle morphology. Our results provide a critical understand-

ing toward tuning the adhesion behavior of nonplanar surfaces

consisting of periodic topographic structures. VC 2010 Wiley

Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 179–185,

2011

KEYWORDS: adhesion; elastomers; interfaces; nonplanar; pat-

terns; surface wrinkling

INTRODUCTION Controlling adhesion is important for mate-rials design in many applications ranging from micro/nano-electronics1 to bioimplants.2 The strategy to achieve suchcontrol can be adapted from Nature. Various organisms inNature precisely control adhesion for locomotion by incorpo-rating geometric features/patterns at the contacting sur-faces.3,4 For example, the gecko, a small lizard, displaysexcellent control of adhesion as a result of novel hierarchicalfeatures on its feet.3,4 Inspired by Nature, topologicalpatterns have been incorporated on the surfaces of manysynthetic materials, and it has been shown that adhesioneither increases or decreases compared with that of thesmooth nonpatterned surfaces.5–8 Although significantunderstanding has been achieved in the context of topologi-cal control of adhesion, most studies have involved planarsurfaces. However, in many real applications, contactingsurfaces can be nonplanar, where fabrication procedure andproper analysis can be challenging. In this article, we investi-gate the adhesion of spherical objects with topological sur-face patterns that are created using surface wrinkling/buck-ling techniques.

Typically, surfaces consisting of random, rough topographydisplay lower adhesion compared with that of smoothsurfaces.9,10 Fuller and Tabor have shown that the adhesionbetween two planar rough surfaces is a balance between thetensile and the compressive loads asperities experience dur-

ing the separation process because of their height differ-ences.10 They applied the Johnson, Kendall, and Roberts(JKR) theory to estimate the adhesion of an individual asper-ity, and the maximum separation force between two roughsurfaces was obtained by summing adhesion responses forall asperities. The change of adhesion was shown to be afunction of a dimensionless adhesion parameter, h, which isthe ratio of the elastic force needed to compress an asperity(approximated as a sphere) of elastic modulus, E, to a depthequal to the standard deviation of the asperity height distri-bution relative to the adhesion force experienced by theasperity. Furthermore, in contrast to the decrease of adhe-sion due to roughness captured by Fuller and Tabor, Briggsand Briscoe reported an enhancement of adhesion for roughsurfaces at certain dimensions of roughness.9

Controlling adhesion behavior of a surface by tuning randomroughness is not trivial, but advancement of various litho-graphic techniques makes it possible to develop surfaceswith regular features/patterns, which can be used for thesepurposes.11 Adhesion of these regularly patterned surfaceshas been widely studied by changing the geometry of thepatterns, including shapes, aspect ratios, and separationbetween the features.6,8,12,13 The increase or decrease ofadhesion strength compared with that of the smooth surfa-ces depends on the local separation mechanism; therefore,interaction/coupling between the pattern features plays an

†Present address: Polymers Division, National Institute of Standards and Technology, Gaithersburg, Maryland.

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important role.6 For noninteracting pattern features withhigh aspect ratios, the adhesion strength is a function ofcontact line, which is equal to the sum contribution of theperimeter of each contact.3,5 For interacting surfaces, theadhesion depends on the nature of the interaction betweenthe patterns and the contacting geometries.6

It is evident that both regularly patterned and random roughsurfaces can display either an increase or decrease of adhe-sion depending upon the surface topology. However, it is notknown whether such changes in adhesion extend to nonpla-nar surfaces. To investigate further, we develop nonplanarpatterned surfaces using surface wrinkling/buckling phe-nomena.14 Surface wrinkling is an alternative to photo orimprint lithography, which are the most common techniquesto introduce geometric patterns but are not easily applied tononplanar surfaces. Wrinkling can be induced by a variety ofmethods, but swelling of a soft substrate constrained by astiff, thin surface layer is convenient5,15 and robust for non-planar geometries. In the work presented here, applying anovel wrinkling technique, we develop wrinkles on soft poly-dimethylsiloxane (PDMS) lenses with a radius of curvature(R) of 7 mm and vary the wavelength (k) and amplitude (A)of the wrinkles from 30 to 70 lm and 0.3 to 5.0 lm, respec-tively. It is noted that k is much smaller than the radius ofcurvature of the curved surface (R). For adhesion experi-ments, we eliminate the effects associated with residualstrain due to wrinkling by using the wrinkled lenses todefine molds from which wrinkled lenses are fabricateddirectly. Hence, our study is significantly different from thatreported by Lin et al.7

Recent studies indicate that the control of adhesion is possi-ble with the incorporation of wrinkles on surfaces.5,7,16

Adhesion of one-dimensional (aligned) wrinkled PDMS sur-faces has been investigated by Lin et al. using a spherical glassprobe, and it was observed that adhesion decreases with theincrease of wrinkle amplitude.7 In comparison, an increase ofadhesion was observed by Chan et al. for two-dimensionalwrinkled PnBA surfaces when a cylindrical glass probe wasused.5 These two studies differ by materials selection, testgeometry, and wrinkle morphology, and a direct comparisonis not possible; however, it is apparent that adhesion behaviorstrongly depends on wrinkle morphology. To further theunderstanding, we vary the wrinkle morphology—both wave-length and amplitude—on a nonplanar PDMS lens and quan-tify the adhesion as a function of wrinkle dimensions. Also,we develop a simple phenomenological model to describe thechange of adhesion, as described by the maximum separationforce, as a function of wrinkle dimensions.

EXPERIMENTAL

Wrinkle Surface FabricationFigure 1 displays the technique for obtaining wrinkled PDMSlenses. We start with a PDMS lens of radius of curvature,R ¼ 7 mm, which is obtained by thermally curing a 10:1mixture of Dow Corning Sylgard 184 oligomer and catalystat 70 �C for 2 h in a concave mold. The cured lens is treatedwith UVO (ultraviolet/ozone) in a Jelight UVO cleaner (model

342, Jelight Company, Irvine, CA) for different durations,ranging from 15 to 60 min, to render a thin silica-likesurface layer. The UVO-treated lens is then placed on a ped-estal in a closed container with a pool of swelling solvent atthe bottom. Swelling of the PDMS lens occurs in the vaporphase. Upon swelling, the UVO-treated surface starts to wrin-kle within a few minutes, and the equilibrium wavelengthand amplitude are reached in a few hours.

During swelling, the modulus mismatch between the PDMSand the silica-like layer results in wrinkle formation. Asdisplayed in Figure 2, as the properties of the silicate layerchange with the increase of UVO exposure time,17 anincrease of wavelength (k) takes place. By varying the UVOexposure time, the wrinkle wavelength is controlled from�20 to 70 lm.

FIGURE 1 Procedure to create wrinkled PDMS lenses.

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Amplitude of the wrinkles (A) scales with the square root ofthe applied strain for a given wrinkle wavelength.14 Theapplied strain, osmotic strain in the present case, iscontrolled by changing the vapor pressure of the swellingsolvents. Ethanol and isopropanol are used as swellingsolvents, and the vapor pressures of these solvents arecontrolled by mixing glycerol at various proportions. Theamplitude is varied from �0.3 to 5.0 lm.

The wrinkled lens is quickly transferred to a pool of com-mercially available UV-curable epoxy-urethane adhesive(Norland 81 Optical Adhesive), which is cured by using UVlight. During curing, the Norland 81 takes the shape ofthe wrinkles, and after removing the PDMS lens from theUV-cured mold, we obtain a mold with exact negative repli-cas of the wrinkled lens. To prepare samples for adhesionexperiments, the negative molds/replicas are filled with amixture of PDMS prepolymer and catalyst (10:1) and arecured thermally at 70 �C for 2 h. The dimensions of the

wrinkles on the replicated PDMS samples are measuredusing an optical profilometer (Zygo NewView 7300).

Contact Adhesion TestAdhesion measurements are performed using a custom-builtcontact adhesion test (CAT) setup. In this setup, a replicatedPDMS lens is brought into contact with a clean glass slide ata speed of 0.5 lm/s. The lens is attached to a custom-designed load cell, and the movement of the lens is preciselycontrolled using a nanopositioner (Exfo Burleigh IW-812).During approach and retreat, the displacement (d) and force(P) are recorded using LabVIEW software. Images of contactarea as a function of time are captured using a CCD camera(Pixelfly) mounted to the microscope (Zeiss Axiovert 200M).

RESULTS AND DISCUSSION

Figure 3(a) displays representative force versus displace-ment measurements obtained from the CAT for two lenses

FIGURE 2 (a) Optical micrograph (left) and three dimensional optical profilometer image (right) of a typical wrinkled PDMS lens.

(b) Wrinkle wavelength as a function of UVO exposure time.



with a similar wrinkle wavelength, k � 70 lm, and with dif-ferent wrinkle amplitudes, A � 5 and 1.5 lm, respectively.The response for a smooth PDMS lens is shown for compari-son purposes. For all experiments, we compress the lensesagainst a glass slide to 30 mN, an arbitrarily defined maxi-mum compressive force, and then reverse the direction ofthe nanopositioner movement. As the lenses are pulled awayfrom the glass slide, a maximum tensile force is exertedbefore the samples detach, and the applied force decreasesto zero. We consider the maximum tensile force, Pmax, as adescriptor for adhesion. In a few cases, the experimentswere performed with different compression loadings, and nosignificant change in separation force, Pmax, was observed. Aswe do not have very high aspect ratio features that canbuckle at high compression loadings, the separation mecha-nism does not change with the applied compression force;hence, Pmax remains independent of the compression loadingwithin the range of wrinkle dimensions studied here.

For a smooth elastic lens under similar conditions, thePmax ¼ (3/2)pGcR, where Gc is the critical energy releaserate and R is the radius of curvature of the lens.18 It can benoticed that for the smaller amplitude (A � 1.5 lm), Pmax ishigher than that observed for the smooth sample; in con-trast, the value of Pmax is smaller for the higher amplitudesample (A � 5 lm). This result indicates that the separationforces can be increased or decreased by changing thewrinkle dimensions. Previous studies by Chan et al.5 and Linet al.7 on wrinkle surfaces captured either an increase ordecrease of separation forces, respectively, whereas in thisstudy, we capture the transition from increase to decrease inthe same material system.

The optical micrographs during the separation process areshown in Figure 3(b). As expected, upon retraction of theprobe, the contact area decreases as a function of time. A

few important observations can be made from these micro-graphs. For the smooth lens, the contact area is a circle witha smooth perimeter, whereas for the smaller amplitude wrin-kles (A � 1.5 lm) the contact area remains almost circularbut the perimeter is no longer smooth. A significant differ-ence is observed for the sample with A � 5 lm, where thecontact area is not continuous and only the crests of thewrinkles contact the glass slides.

Although the representative results in Figure 3 suggest thatadhesion decreases with an increase of wrinkle amplitude,experiments across a range of k and A indicate no cleartrend. Rather as shown in Figure 4, it is evident that fordifferent combinations of k and A, the maximum separationforce can transition from decreased values to enhancedvalues when compared with a smooth lens.

To determine the controlling parameter that dictates thetransition from decreased to increased separation forces, webegin by considering the mechanics of separating a smoothsphere from a rigid surface. This scenario is classicallydescribed by the theory of JKR, who showed that18

Pmax;smooth ¼ 3

2pGcR; (1)

where Gc is the critical energy release rate and R is theradius of curvature of the sphere.

The contact radius, ac, at the maximum force of separation is

ac � GcR2

E�

� �13

; (2)

where E* is the effective modulus such that

1

E� ¼ð1� t2Þ

E; (3)

FIGURE 3 (a) Force versus displacement responses for three representative PDMS lenses. Inset shows a schematic of the experi-

mental setup to measure adhesion. (b) Contact micrographs during separation process.



where E and m are the elastic modulus and Poisson’s ratio ofPDMS, respectively. Here, we consider glass as significantlystiffer than PDMS. The measured modulus of PDMS is 2 MPa,assuming m ¼ 0.5, for all lenses considered here.

From measurements on smooth lenses, Gc equals 0.05 J/m2,which is consistent with reported values in the literature.6,19

For simplicity, we assume that Gc remains approximatelyconstant for all the samples; although it is widely knownthat Gc is a function of velocity for crosslinked PDMS. Forthe low approach and retraction velocity used in our experi-ments, this assumption is reasonable.

To understand the effect of wrinkles on the separation forcesof a soft, elastomeric spherical probe, we consider a simplemodel. We assume the wrinkles to be represented geometri-

cally by a cylinder with radius Rw and length lavg, lyingin the plane of the spherical lens surface, as depicted inFigure 5(a). Based on JKR mechanics, the maximum separa-tion force for a single cylinder from a planar rigid surfacehas been described previously as:20,21

Pmax;c ¼ lavg � pE�a2cw4Rw

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2pE�Gcacw

p� �: (4)

Here, acw is the half-width of an approximate rectangularcontact area at the critical point. It can be shown that acw �(GcR2

w/E)1=3. Therefore, eq 4 can be simplified as

Pmax;c � lavg � ðG2cE

�RwÞ13: (5)

Here, Rw, the radius of curvature of the wrinkles, can bedefined exactly by Rw � f(k A) or more simply in the limit ofA/k ! 0 as

Rw � k2=2p2A: (6)

If we assume that wrinkles act independently at the point ofseparation, then the separation force for n wrinkles is equalto: Pmax,w ¼ n � Pmax,c. Accordingly, the primary challengesfor implementing this simple model are estimating thenumber of ‘‘active’’ wrinkles (n) and the average length (lavg)of the wrinkles.

To estimate n and lavg, we invoke straightforward scaling. Weassume that Rw � R, such that the area of contact at thepoint of maximum separation force is represented by pa2c .Accordingly, the length of a given wrinkle must scale with acas lavg � ffiffiffiffiffiffiffi

pacp

. The number of symmetric wrinkles in contactat the point of separation can be given by nc � 2ac/k.

Upon substitution and further simplification, Pmax,w can beexpressed as:

Pmax;w � a2ck

� �ðG2

cE�RwÞ

13: (7)

Normalizing Pmax,w with Pmax,smooth and substituting for Rw,we find that

Pmax;w

Pmax;smooth� RGc

kAE�

� �13

� RA

k2� GckA2E�

� �13

� RA

k2

� �13

x (8)

Here, (RA/k2)1=3 is a dimensionless geometric parameter that

relates the radius of curvature of the PDMS probe to theamplitude and wavelength of the wrinkles. The parameter xis equal to (Gck/A

2E*)1=3, which is a ratio of adhesion force to

elastic force the wrinkles experience. It is noted that thedimensionless number, x, is very similar to the adhesionparameter (h) presented by Fuller and Tabor, x � (1/h)

1=3.10

Similar to x defined here, h is the ratio of the elastic forceneeded to compress an asperity (approximated as a sphere)of elastic modulus (E) to a depth equal to the standard devi-ation of asperity height distribution to the adhesion forceexperienced by the asperity.

FIGURE 4 Normalized maximum separation force as a function

of wavelength, k (a) and amplitude, A (b). An individual data

point represents an average of a minimum of three adhesion

experiments on the same sample. The error associated with

the measurements is smaller than the symbol size.



Experimental data after normalization are shown in Figure5(b), and a reasonable fit with eq 8 is obtained. The scatterin Figure 5 is likely due to small changes in wrinkle arrange-ment, which is not accounted for in the phenomenologicalmodel. Also, it is important to mention that this model con-siders the wrinkles as discrete noncollapsible cylinders, thatis, the cylinders do not deform to create a continuouscontact area [as observed for high-amplitude wrinkles inFig. 3(b)]. However, the model captures the general trend,even for the collapsed wrinkles. A model that specificallycaptures the collapsed wrinkles will be presented in future.

SUMMARY

In this article, we use a surface wrinkling technique tocreate patterns on nonplanar surfaces. We control wrin-

kle dimensions to change the maximum separationforces of PDMS lenses. A transition from enhancementof adhesion to decrease is observed depending uponthe wrinkle dimensions. A simple model is proposedthat describes the change of adhesion behavior as afunction of wrinkle morphology. Compared with theplanar surfaces, where adhesion is determined by thecontact line or the sum contribution of the perimeterof each contact, adhesion of nonplanar wrinkled surfa-ces depends on the cumulative effect of the radius ofcurvature of the curved surface, the wavelength, andthe amplitude of the wrinkles. Our results provide a criticalunderstanding toward tuning the adhesion behavior of non-planar surfaces consisting of periodic topographic surfacefeatures.

FIGURE 5 (a) Typical contact of a cylinder against a glass slide. An individual wrinkle is approximated as a cylinder. (b) Normalized

maximum separation force as a function of x.



ACKNOWLEDGMENT

S. Kundu, T. Long, and A. J. Crosby acknowledge the Cen-ter for University of Massachusetts/Industry Research onPolymers for funding and Edwin P. Chan for helpfuldiscussions.

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Adhesion of nonplanar wrinkled surfaces

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