“contact” of nanoscale stiff films

“Contact” of Nanoscale Stiff FilmsFut K. Yang, Wei Zhang, Yougun Han, Serge Yoffe, Yungchi Cho, and Boxin Zhao*

Department of Chemical Engineering and Waterloo Institute for Nanotechnology, University of Waterloo, 200 University AvenueWest, Waterloo, Ontario, Canada N2L 3G1

ABSTRACT: We investigated the contact behaviors of ananoscopic stiff thin film bonded to a compliant substrate andderived an analytical solution for determining the elastic modulusof thin films. Microscopic contact deformations of the gold andpolydopamine thin films (<200 nm) coated on polydimethylsilox-ane elastomers were measured by indenting a soft tip andanalyzed in the framework of the classical plate theory andJohnson−Kendall−Roberts (JKR) contact mechanics. Theanalysis of this thin film contact mechanics focused on thebending and stretching resistance of thin films and isfundamentally different from conventional indentation measure-ments where the focus is on the fracture and compression of thefilms. The analytical solution of the elastic modulus of nanoscopicthin films was validated experimentally using 50 and 100 nm goldthin films coated on polydimethylsiloxane elastomers. The technical application of this analysis was further demonstrated bymeasuring the elastic modulus of thin films of polydopamine, a recently discovered biomimetic universal coating material.Furthermore, the method presented here is able to quantify the contact behaviors of nanoscopic thin films, effectively providingfundamental design parameters, the elastic modulus, and the work of adhesion, crucial for transferring them effectively intopractical applications.

1. INTRODUCTIONAs future technological innovations gear toward miniaturizingmachines and maximizing performance density, thin filmsbecome one of the most important structures that enable theuse of nanomaterials for a diverse range of innovativeapplications including optics, energy conversion and storage,electronics, and biomedical applications.1−4 The assembly ofvarious nanomaterials into a thin film enables the creation ofmultifunctional structures with synergetic properties. Layeredsystems made of stiff films coated on compliant substrates areof growing commercial interests. For example, thin sheets ofnoble metals and semiconductors bonded to soft substrateshave recently found applications in flexible electronics,including surgical and diagnostic implements that naturallyintegrate with the human body, cameras that utilize biologicallyinspired designs to achieve superior performance, and wearablecommunication devices.5−8

Mechanical failure poses a significant engineering challengein the development of functional devices consisting of layeredstructures. When stretched or bent, the substrate deforms, butthe bonded film may crack or delaminate due to the substantialelastic mismatch and weak adhesion at the interface. Figure 1ashows an SEM image of cracks and delamination of 100 nmgold thin film coated onto a polydimethylsiloxane (PDMS)elastomer (Figure 1b), a typical component for the develop-ment of biointegrated devices.9−12 The elasticity of a stiff thinfilm is a key predictor of the mechanical stability for effectiveintegration and utilization in practical applications.11,12

However, there are only a few options for measuring theelasticity of nanoscopic thin films. One of the most prevailingoptions is nanoindentation (Figure 2a,i), in which a hardpointed tip is pressed into a relatively soft thin film bonded to arigid substrate, where the properties of the film is determinedby the elastic recovery of the indent upon unloading of theprobe.13 As the elastic field under the indenter is not confinedto the film itself but extends to the substrate, interpretation ofthe experimental data becomes increasingly demanding as thefilm gets thinner (i.e., < 200 nm)14 and as the mismatch of theelasticity between the film and the substrate gets larger. This isespecially the case when the substrate is softer than the filmsince one can no longer assume the film hardness is constantwith respect to the indentation depth until the tip reaches thefilm−substrate interface.15,16 In these cases, complex mathe-matical treatments based on numerical analysis or material-specific modeling must be applied to obtain meaningfulresults.17,18 A more recent option exploits a buckling instabilitythat occurs in the bilayer consisting of a stiff thin film coatedonto a relatively compliant thick substrate (Figure 2a,ii), ofwhich, the effective elastic modulus of the thin film isdetermined by analyzing the spacing of the highly periodicwrinkles appeared on the film surface via buckling mechanics.19

It is an elegant method, but it lacks the versatility of indentation

Received: April 4, 2012Revised: May 20, 2012Published: May 22, 2012

Article

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© 2012 American Chemical Society 9562 dx.doi.org/10.1021/la301388e | Langmuir 2012, 28, 9562−9572

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techniques that allow the measurement of a range ofmechanical responses of material systems by varying loads,contact sizes, and indentation depths.The microindentation method (Figure 2a,iii) is widely used

in the study of contact deformations and the measurements ofinterfacial adhesion in the framework of contact mechanicstheories.20−22 It is able to provide insights on molecularinteractions between the adhering surfaces23 and on biologicalprocesses such as cell migration and differentiation.24−28 Therehas also been a continuing interest in the application ofmicroindentation to quantify the mechanical property ofcoatings, thin films, and multilayered structures includingmicroelectronics, optical systems, and microelectromechanicalsystems (MEMS).29 In this article, we used the micro-indentation to investigate the contact behaviors of nanoscalestiff films and hypothesized that the elastic modulus of thenanoscopic thin film can be determined by measuring andanalyzing its microscopic “contact” behaviors. The micro-indentation analysis established in this article focused on thestiff thin film bonded on a soft substrate (similar in geometry tothe buckling method) and has the indentation features (similarto the nanoindentation) allowing the measurement ofmechanical responses at varied loads, contact sizes, andindentation depths. We first derived an analytical solution fordetermining the effective elastic modulus of thin films by

extending the Johnson, Kendall, and Roberts (JKR) contactmechanics30 with the classical plate theory to accommodate themechanics of the thin films. Second, we reported a set ofindentation experiments on PDMS substrates coated with goldthin films to investigate “contact” behaviors of gold thin films interms of its elasticity and contact deformations using thedeveloped analysis and established a methodology that could beapplied to other systems. Third, we applied the analysis andmethod to determine the elastic modulus and the surfaceadhesion of a recently discovered biomimetic universal coatingmaterial,31 polydopamine, whose properties are not well-understood but which has great potential for applications, i.e.,to serve as a nanometer thin ad-layer for biointegration,32−35

for biomineralization,36,37 or for biosensing.38,39 The technicalimplication of the effective elastic modulus as it relates to theintegration and application of nanomaterials is also discussed.

2. EXPERIMENTAL SECTIONMaterials. PDMS, Sylgard 170, and Sylgard 184 were supplied by

Dow Corning Corp., Midland, MI. Each PDMS contains twoelastomer components. The opaque fillers in Sylgard 170 wereremoved by centrifugation and only the remaining clear solution wasused. Plain microscope slides were supplied by Fisher Scientific andwere cleaned with acetone and ultrapure water before use. Dopaminehydrochloride was supplied by Sigma-Aldrich. TRIS-HCl buffer base(BP152) was supplied by Fisher BioReagents.

Figure 1. (a) A typical SEM image of cracking and delamination of a 100 nm gold film coated on a flat compliant PDMS substrate under themicroscopic contact of a hemispherical compliant PDMS tip; the tip was coated with 5 nm gold coating for SEM imaging and subject to acompressive load (∼ 0.1 N). (b) Optical image of gold sputtered PDMS substrate.

Figure 2. (a) Characterization techniques for nanoscopic thin films. Setup of the microindentation system: (b) microindenter; (c) bottom-viewoptical images of the contact area; and (d) side-view of a PDMS tip indented on a gold coated PDMS substrate.

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dx.doi.org/10.1021/la301388e | Langmuir 2012, 28, 9562−95729563

Preparation of Flat Substrates and Hemispherical Tips ofPDMS. PDMS solution was prepared by mixing the two elastomercomponents at a weight ratio of 1:1 for Sylgard 170 and 10:1 forSylgard 184 according to the specifications recommended by themanufacture. The flat sheet of PDMS was made by casting 2 mL ofPDMS solution onto a microscope slide and curing at 90 °C for 2.5 hin ambient air. The sheet thickness was measured to be 1.25 ± 0.1mm. The hemispherical tip of PDMS was made by first molding thePDMS solution into a hemispherical shape using a custom-madeTeflon mold and curing the tip at 90 °C for 15 min. To smooth the tipsurface, the tip was coated with a layer of PDMS solution for Sylgard184 and with three layers for Sylgard 170 with 10 min of curing for thefirst two layers. Afterward, the coated tip was cured at 90 °C for 2.5 hin ambient air. The tip radius was measured to be 2.8 ± 0.1 mm forSylgard 184 and 3.0 ± 0.1 mm for Sylgard 170 by analyzing the side-view image of the tip using a custom-written MATLAB (R2008a,MathWorks) script, which gives a least-squares best-fit to the curvatureof the apex of the tip.Deposition of Gold Thin Films. Gold thin films were deposited

on PDMS samples in a magnetron sputter-coater (Denton VacuumDesk II) at 15 mA at the room temperature. The samples werepretreated with UV/Ozone (Novascan Digital UV Ozone System) for15 min to improve interfacial adhesion. The thickness of the depositedfilm was controlled by deposition time at 5 nm min−1 and wasconfirmed by an atomic force microscope (AFM) and a stylusprofilometer (Veeco DekTak 8) on glass substrates to be 101 ± 2 nmfor 20 min of deposition time. The surface quality of the film wasexamined by a scanning electron microscope (SEM; Zeiss LEO 1550),and the topology showed the surface was uniform with no apparentcrystallographic texture. The crystallinity of gold thin film on PDMSwas examined by an X-ray diffractometer (PANalytical MRD XpertPro) using line scan and powder mode.Coating of Polydopmine Thin Films. Dopamine solution was

prepared by dissolving 2 mg mL−1 of dopamine hydrochloride in a 10mM TRIS-HCl buffer at pH 8.5. PDMS samples were submerged inthe dopamine solution for a period of 24 h. To avoid the deposition ofpolydopamine nano/microparticles formed in the solution during thecoating process, all samples were placed upside down. The coatedsamples were rinsed with ultrapure water and dried in air overnight.The surface quality of the coatings was examined by opticalmicroscope (Omano OMM300T). It was difficult to measure thethickness of the coating accurately because the substrate is soft. Unlikethe gold sputtering process, the growth of polydopamine is stronglyinfluenced by the surface chemistry of the substrate, where thethickness of polydopamine has been reported on different substratesranging from less than 20 nm to over 70 nm for the same dopamineconcentration and deposition time.40,41 Hence, we cannot measure thethickness of the thin film using a different rigid substrate as we did forgold thin films. To our knowledge, the thickness of polydopaminecoated on PDMS has not been reported. We employed twoexperimental techniques and the thickness of polydopamine wasmeasured to be 67 ± 5 nm by AFM (Pacific Nanotechnology AFMNano-R) and 70 ± 20 nm by optical profiler (Veeco WYKONT9100). As a result, we took the whole number 70 nm as areasonable estimate for the polydopamine thickness.Indentation Measurements. Contact deformation measurements

were carried out using a custom-made microindentation system that iscomprised of a linear stage (Newport MFA-CC), a 25 g forcetransducer (Transducer Techniques GS0−25), and an inverted opticalmicroscope (Omano OMM300T) and controlled by a LabVIEW(version 8.5, National Instruments) program. Hemispherical PDMStips were used as the indenters. In comparison to a rigid indenter ofhemispherical or cylindrical shape, the soft PDMS tips in hemi-spherical shape give a large contact area and have no such problem ofmechanical misalignment during indentation; moreover, the loadversus contact area data can be readily interpreted using the classicalJKR contact mechanics theory. The PDMS tips were brought intocontact with substrates of PDMS at a speed of 0.1 μm sec−1 until apreload force was reached. The substrates were then coated with goldor polydopamine, and the indentation was repeated on the same

contact spots using the same tip. Force, displacement, images of thecontact area, and time information were recorded. Static indentationswere also conducted on gold-coated samples with the tip moving at 0.1μm sec−1 between steps and holding for 180 s at each step to checkwhether the indentation meets the equilibrium assumption of JKR. Nosubstantial changes in contact areas or forces were detected at eachstep during loading, suggesting the loading speed of 0.1 μm sec−1 wasquasi-equilibrium. At least four independent measurements were madefor each test condition.

Contact Angle Measurements. The static contact angles weremeasured on polydopamine-coated PDMS substrates by the sessiledrop method with a set of probe liquids. Each probe liquid, 5 μL involume, was dispensed on the substrate from a height of 2 cm inambient air at the room temperature. The side view of the liquid dropwas recorded after the drop had stopped spreading (within 1 min),and the associated contact angles were analyzed by a custom-madeMATLAB (R2008a, MathWorks) script.

3. RESULTS AND DISCUSSIONThe contact behaviors of nanoscale stiff films (gold andpolydopamine) coated on PDMS elastomers were investigatedusing microindentation measurements as shown in Figure 2b−d; the applied load and the contact deformations were analyzedin the framework of JKR contact mechanics and the platetheory.

3.1. Theoretical Analysis. In the previous microindenta-tion studies,42−47 compliant thin films are bonded to relativelystiff substrates, and the mechanical property of the film isdetermined by compression or, in other words, is determinedfrom the film’s shortest dimension (thickness), making themechanics only applicable to thick films that are on the order ofmicrometers. The physical situation is the opposite in ourinvestigation, which focuses on the contact mechanics of ananoscale stiff thin film bonded to a thick compliant substrateindented by a soft hemispherical tip. Upon indentation, the filmis stretched and bent instead of being compressed. This allowsfor determining the mechanical property of the film from itslongest dimension (length), making the mechanics applicableto nanoscale thin films. To establish a context for our analysis,we briefly describe the theoretical basis of the JKR contactmechanics and then apply it in combination with the platetheory to the nanoscale film coating system.The classical JKR contact mechanics describes the contact

behavior of elastomers. It balances the elastic energy associatedwith the deformation of the bodies, the potential energyassociated with the displacement of the bodies, and the work ofadhesion associated with the contact of the bodies.30 When twospherical bodies of radius Rtip and Rsub and of effective elasticmodulus Etip* and Esub* are in contact, the relation between theapplied load Psys, the work of adhesion Wsys of the two surfaces,and the radius of contact area a can be expressed by

π= − =*

− *

* = * + *

= +

−

−

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

P P PE a

Ra W E

EE E

RR R

4

38

1 1

1 1

sys syse

sysa sys

3

sys

3sys sys

systip sub

1

systip sub

1

(1)

Psys can be split into two independent components: an elasticcomponent Psys

e and an adhesive component Psysa . If the

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substrate is flat, the combined radius Rsys becomes the radius ofthe tip (Rsys = Rtip). The effective elastic modulus E* is relatedto the Young’s modulus E and the Possion’s ratio ν by

* =−

EE

v1 2 (2)

It is worthwhile to note the assumptions behind the JKRcontact mechanics:48 (i) the system is in equilibrium; (ii) thecontact deformation is small compared to the size of the bodies,so that (a) the bodies can be considered as a mathematical half-space, (b) parabolic approximation can be assumed for theprofile of spheres as the contact radius is much smaller than theradius of the bodies, and (c) the radial displacement u due todeformation is much smaller than the normal displacement w;and (iii) elastic and adhesive forces are confined within thecontact area, meaning that the normal stress is zero outside ofcontact area and the molecular interfacial forces areinfinitesimally short-ranged.We extended the JKR contact mechanics to accommodate

the mechanics of a stiff thin film bonded to a compliant flatelastic substrate. Upon indentation, the film is stretched andbended while the softer substrate takes up the compressivedeformation. We denote this extension “thin film contactmechanics”. Our analysis started with the fact that when thefilm is harder than the substrate, the deformation of thesubstrate is constrained by the film such that a higher appliedload is required to reach the same contact radius as that of thedeformation of the uncoated substrate. The deformation isillustrated in Figure 3a, where the three geometric parameters,R, a, and h, are the tip radius, the contact radius, and the filmthickness, respectively. We assume the coated substrate will actas a homogeneous half-space when indented in the normaldirection; that is, the bulk effective elastic modulus of thecoated substrate is constant. The assumption has been shownto be reasonable for thin films coated onto a substrate with alow elastic modulus (E < 10 MPa) and when the ratio ofcontact radius to film thickness is large (a/h > 20).49,50 Thus,we can directly apply eq 1 to a thin film bonded system, wherethe subscript “(f)” indicates “with thin film”, and Rsys = Rsys(f),since the influence of the thin film coating on Rsys is negligible.

π= − =*

− *

* = * + *

= +

−

−

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

P P PE a

Ra W E

EE E

RR R

4

38

1 1

1 1

sys(f) sys(f)e

sys(f)a sys(f)

3

sys

3sys(f) sys(f)

sys(f)sub(f) tip

1

syssub tip

1

(3)

Due to the resistance of the film to deformation, there will bea difference in load or an extra load Pf to reach the same contactarea between coated and uncoated substrates. The Pf can bedetermined by subtracting P′sys from Psys(f) as shown in eq 4.The P′sys is the load applied to induce the same contactdeformation if the film is infinitely soft producing zero elasticresistance; that is, P′sys ≈ Psys in eq 1, except the work ofadhesion is Wsys(f) instead of Wsys.

π= − ′ = −*

+ *P P P PE a

Ra W E

4

38ff sys(f) sys sys( )

sys3

sys

3sys(f) sys

(4)

The classical plate theory is applied to analyze the contactmechanics of the film as its dimensions and deformation fit thedefinition of a plate. A plate is a flat noncurved solid whosethickness is at least 1 order of magnitude smaller than thesmallest of its other dimensions; it deforms by bending and bystretching when its normal deflection or displacement is largerthan one-fifth of its thickness.51 On the basis of the firstassumption of JKR, the mechanical balance of the film can bedescribed using a simplified form of von Karman’s equation fora symmetric plate.51

∫

+ −

= + + + *⎜ ⎟

⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥

wr r

wr r

wr

hwr

ur

vur

wr h E r

p r r r

dd

1 dd

1 dd

12 dd

dd

12

dd

12( ) d

r

z

3

3

2

2 2

2 f

2

3f 0

(5)

w is the normal displacement of the film under the appliednormal stress pz(r), u is the radial displacement, r is the radialdistance from the center of contact, and νf, Ef*, and h are the

Figure 3. Schematics for (a) the contact deformation of a soft spherical tip indented on a soft flat substrate coated with a stiff thin film and (b) thebending of the nanoscopic stiff film.

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Possion’s ratio, the effective elastic modulus, and the thicknessof the film, respectively. With respect to the second assumptionof the JKR contact mechanics,

≪ →=

=⎧⎨⎩u w

uu r

0d /d 0 (6)

Equation 5 becomes

∫

+ −

= + *⎜ ⎟⎛⎝

⎞⎠

wr r

wr r

wr

hw

dr h E rp r r r

dd

1 dd

1 dd

6 d 12( ) d

r z

3

3

2

2 2

2

3

3f

0

(7)

In JKR contact mechanics, the contact deformation due tointerfacial adhesion follows a profile of uniform normaldisplacement (flat punch geometry),48 so the curvature ofdeformation within the contact area depends solely on theelastic behavior of the system. Accordingly, the curvature is thesame as in adhesionless (Hertzian) contact under an appliedload equal to Pe, and the deformation is spherical and has aradius R+as illustrated in Figure 3a. This radius can becalculated by eq 3 as an equivalent radius of a “perfectly rigid”tip (Etip* = ∞ → Esys* = Esub* ).52

π=

*=

*

+ *+R

E a

P

E a

P a W E8

43 sub(f)

3

sys(f)e

43 sub(f)

3

sys(f)3

sys(f) sys(f) (8)

Accordingly, the normal displacement of the film w is relatedto the radial distance r, as shown in Figure 3b, where c is aconstant

= − − ≤ ≤+w R r c r a( ) for 02 2(9)

Substituting the derivatives of dw/dr in eq 7 and rearrangingthe equation, we obtain

∫ = * − + + −−

+ +

+p r r r E hr r R h r h r R

R r( ) d

6 6 ( ) 4 ( )12(( ) )

r

z0f

6 4 2 2 4 2 2 2

2 2 5/2 (10)

Since the film is bonded and therefore is fully compliant tothe deformation of the substrate, we can apply the thirdassumption of JKR (i.e., all normal stresses are confined within

the contact area) to define the limit of the integral in eq 10.With respect to the contact area, the extra load Pf is

∫π

π

=

= * − + + −−

+ +

+

⎛⎝⎜

⎞⎠⎟

P p r r r

E ha a R h a h a R

R a

2 ( ) d

6 6 ( ) 4 ( )6(( ) )

a

zf0

f

6 4 2 2 4 2 2 2

2 2 5/2

(11)

When the film is equal to or softer than its substrate (Ef* ≤Esub* ), the applied load calculated from eq 11 is very small but isnot zero as indicated by eq 4. The discrepancy is due to the factthat when the substrate is harder, the film deformation isdominated by compression, violating the basic premise of theplate theory by making the film thickness a variable. In general,the higher the Ef*/Esub* ratio, the more accurate the analyticalsolution is.As shown in eq 11, the thin film contact mechanics can be

applied to measure the effective elastic modulus of thin films Ef*if the extra load Pf and the geometric parameters, R+, h, and a,are known. The modulus can be experimentally obtained bycomparing a system with and without bonded film using eq 4and fitting the extra load with eq 11. This procedure will bedemonstrated in the following sections on the indentationexperiments of gold sputtered PDMS substrates. Since theeffective elastic modulus of polycrystalline gold thin films (40nm < h < 800 nm) has been determined to be close to that ofbulk gold (which is well-documented to be 98 GPa, where theYoung’s elastic modulus E = 79 GPa and Possion’s ratio ν =0.44) by nanoindentation and other characterization techni-ques,53−55 this set of experiments also aimed at validating thenewly developed thin film contact mechanics, i.e., eq 11.

3.2. Microindentation on Gold Thin Films. Inindentation tests, hemispherical PDMS tips were first broughtinto contact with substrates of PDMS at a quasi-equilibriumspeed of 0.1 μm sec−1 until a preload of 5 mN was reached.Afterward, the substrates were pretreated with UV/ozone for15 min and then sputtered with gold thin films of nanometerthickness. Subsequently, the indentation was repeated with thesame tip. The pretreatment is necessary to enhance theadhesion at the gold-PDMS interface without affecting themechanical properties of PDMS within the error of theexperiment. We noticed that, without the pretreatment, the

Figure 4. Characterization of gold thin films: (a) typical AFM measurement on the thickness of the 50 nm gold thin film sputtered on glass; (b)typical SEM scan of the 50 nm gold thin film coated on PDMS at low (left) and high resolution (right); and (c) typical X-ray diffraction spectra of 50nm gold thin film bonded on PDMS.

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slippage at the interface would result in a much smaller contactarea and thus give a lower Esys(f)* than it should be. Two types ofPDMS, Sylgard 170 and 184, were used; the elastic modulus of184 is about 4 times higher than that of 170. The experimentaldata were analyzed with the JKR contact mechanics (eqs 1 and3) and the thin film contact mechanics (eqs 4 and 11). Theexperimental setup is illustrated in Figure 2b−d. An AFM andstylus profiler, SEM, and X-ray diffractometer were used tocharacterize the thickness (Figure 4a), surface quality (Figure4b), and crystallinity (Figure 4c) of the gold thin film,respectively. The gold thin film on PDMS appeared to beuniform with no specific crystallographic texture, and the X-raydiffraction pattern confirmed that the film was polycrystallinewith a preferred orientation in the {111} direction. There werealso no cracks on the sputtered gold film, suggesting there wasno residual stress in the film.The engineering strain εe of the film was estimated by eq 12

to ensure its deformation by bending and stretching is elastic;thin film contact mechanics does not account for plasticity.

ε = Δ =−+ −

+( )LL

R a

a

sin aR

e

1

(12)

L is the length of the arc of deformation and the unit of theinverse sin is in radian. The engineering strain of the gold thinfilm was estimated to be 0.01% to 0.05% during indentation.Most materials obey Hooke’s law to a reasonable degree thatthey do not deform plastically until a certain strain is reached.The typical strain for bulk ductile metals is around 0.01%.56

This strain increases when the plastic flow of atoms isconstrained by physical dimensions. For a gold film, the strainis more than 0.2% when its thickness is reduced to 800nm.57−59 Hence, the deformation of the gold thin film duringindentation is linearly elastic, and the use of our analyticalsolution is justified.Figure 5a shows the cubic contact radius versus force curves

for microindentations with and without the bonded film. Thecontact area of the coated substrate was significantly smallerthan the one without coating at the same applied load,indicating the film had constrained the deformation of thesubstrate (Figure 5b,c). The experimental data fit well with JKRcontact mechanics even for coated samples. This supports ourassumption that the coated substrate would behave like ahomogeneous half-space. The resulting work of adhesion Wsys,

effective elastic modulus of the system or combined modulusEsys* , and effective elastic modulus of (coated and uncoated)substrates Esub* are summarized in Table 1.

The work of adhesion Wsys of uncoated Sylgard 170 wasmeasured to be 41.5 mJ m−2. This value is well within the rangeof 40 to 44 mJ m−2 found in the literature for pure PDMS.60−62

The work of adhesion for uncoated Sylgard 184 is 36.7 mJ m−2,which is lower than that of Sylgard 170. The lower work ofadhesion on Sylgard 184 might be because it is not a purePDMS, as it contains reinforcing silica fillers; this value is closeto that determined by contact angle measurements, which gavea surface energy of 19 mJ m−2 or a work of adhesion of 38 mJm−2 for Sylgard 184.63 The combined effective elastic modulusEsys* of uncoated 184 is 1.66 MPa, about 4 times higher thanthat of 170 equal to 0.442 MPa. Compared to uncoatedsamples, the coated ones showed a lower work of adhesion anda higher elastic modulus. Despite the significant difference insubstrate elasticity, the combined modulus Esys* is about 0.05MPa higher with 50 nm gold-coated Sylgard 170 and 184 thanthose of uncoated ones. Doubling the film thickness to 100 nmfurther increased the modulus by about 0.02 MPa. The effectiveelastic modulus of the substrate Esub* with and without film canbe calculated from the combined one as both the tip and thesubstrate are of the same material and thus have the sameelasticity; the determined effective elastic moduli of thesubstrates Esub* are listed in the second column of Table 1.

Figure 5. Comparison between gold coated and uncoated substrates: (a) cubic contact radius (a3) versus load (P) curves of a hemispherical PDMStip indented on a flat PDMS (Sylgard 170) substrate with and without 50 nm gold thin film (170(G50) and 170) and (b,c) the associated bottom-view optical images of the contact areas with and without coating at an applied load of 0.3 mN.

Table 1. Parameters Obtained from the JKR Fitting in Figure5aa

Esys* (MPa) Esub* (MPa) Wsys (mJ m−2)

170 0.442 ± 0.001 0.884 ± 0.001 41.5 ± 0.5170(G50) 0.492 ± 0.005 1.108 ± 0.023 35.0 ± 1.3170(P70) 0.459 ± 0.010 0.954 ± 0.044 39.0 ± 1.2184 1.66 ± 0.02 3.31 ± 0.04 36.7 ± 0.8184(G50) 1.71 ± 0.01 3.51 ± 0.05 31.0 ± 0.2184(G100) 1.73 ± 0.02 3.65 ± 0.07 33.8 ± 0.1

aWork of adhesion (Wsys), combined effective elastic modulus of thesystem (Esys* ), and calculated effective elastic modulus of the substrate(Esub* ) for indentations of PDMS tip on PDMS (Sylgard 170 or 184)substrate with and without 50 nm gold, 100 nm gold, or 70 nmpolydopamine thin films (G50, G100, or P70).

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Figure 6a plots the extra load Pf against the contact radius a.The extra load Pf is calculated by eq 4. On the basis of theradius of the contact deformation R+ calculated by eq 8 and byvarying the effective elastic modulus of the film Ef*, the elasticbehavior was also fitted by the plate theory with eq 11, wherethe fitting is displayed as a solid line in the plot. Experimentaldata was substituted in equations wherever possible tominimize the use of JKR fitting parameters. Taking eq 8 asan example, Psys(f)

e in the equation can be calculated in twoways: one way is to substitute the fitted parameter Esys(f)* andcalculate it as 4Esys(f)* a3/3Rsys; the other way is to substituteexperimental data Psys( f) and calculated it as Psys( f) + Psys(f)

a . Thelatter approach is used for these experiments. Even though eq 4and eq 11 have completely different formulations, they matchreasonably well with each other, as shown in the plot,suggesting the analytical solution is self-consistent. Note thatthe Esys(f)* was determined according to the homogeneous half-space assumption, representing an average of the data used infitting, and, accordingly, the fitting of thin film contactmechanics should be carried out on the same data set that isused in JKR for consistency. The main purpose behind the useof Esys(f)* is to determine the work of adhesion Wsys(f) in eq 3,which is then used to calculate the extra load Pf in eq 4. It has

been shown from finite element calculations that when thecontact radius a is orders of magnitude larger than the filmthickness h, which is the case in this study, the error associatedwith the calculation of the work of adhesion Wsys(f) using Esys(f)*is insignificant.49,50 The effective elastic moduli of gold thin filmEf* determined for different samples are shown in Figure 6b.They are in good agreement with each other and with thedocumented gold modulus of 98 GPa despite the substantialchanges in substrate elasticity and coating thickness betweenthe samples, validating our analytical solution and theassociated method. Although we have not examined otherfilm thicknesses, we expect the technique to be fairly accurateup to 200 nm (where a/h > 103) based on literatureinformation.49,50

Since cracks are commonly presented on bonded thin films,additional tests were performed to investigate the effect ofcracks on the measurements of contact area and theapplicability of the developed thin film mechanics to thinfilms with cracks. Note that there were no cracks present on thegold thin films in our study. Tests were carried out to examinethe deformation of 100 nm gold thin films with and withoutcracks by first indenting on a flawless spot, then introducingcracks to the spot by stressing the film at a point distant from

Figure 6. (a) Plot of the extra load (Pf) versus contact radius (a) for PDMS (Sylgard 170) substrate coated with 50 nm gold thin film. (b)Determined effective elastic modulus for 50 and 100 nm gold thin films coated on PDMS substrates (170(G50), 184(G50), and 184(G100)). Datain the plot are generated based on the difference in the elasticity of the system with and without the film (open circles) and are fitted based on theplate theory (solid line) with the substitution of experimental data.

Figure 7. Comparison of contact deformations of 100 nm gold coating on PDMS (Sylgard 170) substrates (a) with and (b) without artificiallyintroduced cracks on the same contact spot using the same tip at different applied loads during microindentation.

Langmuir Article


the contact area, and finally reindenting on the same spot withthe same tip. As shown in Figure 7, the size of the contact areaat the same applied load was visibly unchanged with andwithout cracks, suggesting that cracks have negligible influenceon the microindentation data. Perhaps, the influences of thediscontinuity of the film were lessened by the underlyingcontinuous soft substrate because the film was fully bonded tothe substrate.3.3. Microindentation on Polydopamine Thin Films. A

second set of experiments was performed on PDMS substratescoated with polydopamine thin films. Dopamine has a chemicalstructure of catecholamine mimicking the chemical composi-tion of mussel adhesive proteins, which have unusually highconcentrations of catechol and amine functional groups.30

Under alkaline conditions, the catechol functional group can beoxidized to quinone allowing dopamine to self-polymerize andform nanometer thin films on support surfaces. The facts thatpolydopamine can self-polymerize and coat on virtually anymaterials and the resulting film can support a variety ofreactions make polydopamine an attractive multifunctionalcoating.30 Thus far, its adhesion and mechanical properties arenot well studied. Our preliminary results showed thatpolydopamine thin films are brittle and develop cracks whencoated on soft substrates.64 Here, we apply the thin film contactmechanics to gain insights on the properties of 70 nmpolydopamine thin films coated on flat PDMS substrates. Incontrast to coating with gold thin films, no UV/ozone

pretreatment of the PDMS surface was needed. We haveapplied the same approach as employed in the gold thin filmexperiments to evaluate the effective elastic modulus, and alsothe surface adhesion, of polydopamine thin films. Indentationon polydopamine thin films was repeated several times withoutleaving any visible impacts on the integrity of the film (no newcracks) and on the experimental data collected, suggesting thatthe films were strongly bonded to the substrate and were fairlyrobust.Figure 8a shows the typical cubic contact radius versus force

curves for microindentations with and without the bondedpolydopamine film. The curves were fitted by JKR contactmechanics, and the resulting parameters are listed in Table 1.The work of adhesion between polydopamine and Sylgard 170was determined to be 39 mJ m−2. A set of probe liquids weredispensed on the surface of polydopamine coated PDMSsubstrate, and the resulting contact angles as shown in Table 2were interpreted for surface free energy γ according to van Oss’method65 or Wu’s method66 with water as one of the pairingparameters. The results were consistent with that of literature.40

From the energy components of the surface free energy, thework of adhesion between polydopamine and PDMS wasestimated to be 49.9 mJ m−2 when van Oss’ method is used or43.2 mJ m−2 when Wu’s method is used. These values arecomparable to the one obtained by JKR contact mechanics, 39mJ m−2, suggesting that the work of adhesion obtained frommicroindentation is reasonable. It is important to note that the

Figure 8. Comparison between polydopamine coated and uncoated substrates: (a) cubic contact radius (a3) versus load (P) curves of ahemispherical PDMS tip indented on a flat PDMS (Sylgard 170) substrate coated with and without polydopamine thin films and (b) the plot ofextra load Pf versus contact radius a; the solid line is the fitting based on thin film contact mechanics. Data in the plot are generated based on thedifference in the elasticity of the system with and without the film (open circles) and are fitted based on the plate theory (solid line) with thesubstitution of experimental data.

Table 2. Surface Energy of Polydopamine Films Determined from Contact Angle Measurementsa

γLW γAB γ+ γ− γ (mJ m−2) θ (°)

diidomethane 50.8 0.0 0 0 50.8 51.2 ± 2.6DMSO 36 8.0 0.5 32 44 23.3 ± 1.9ethylene glycol 29 19.0 1.92 47 48 43.3 ± 1.2formamide 39 19.0 2.28 39.6 58 42.5 ± 2.6glycerol 34 30.0 3.92 57.4 64 67.2 ± 4.5hexadecane 27.5 0.0 0 0 27.5 16.4 ± 1.2water 21.8 51.0 25.5 25.5 72.8 64.8 ± 3.7polydopamineVan Oss 30 ± 3.9 10 ± 5.0 1.4 ± 1.4 17.7 ± 4.3 40 ± 8.9Wu 22.5 ± 8.9 22.2 ± 5.7

aThe contact angles (θ) were obtained on polydopamine coated PDMS substrates using different liquids and were interpreted according to the VanOss and Wu methods with water as one of the pairing parameters.

Langmuir Article


deviation in adhesion values between microindentation andcontact angle measurements is not unexpected. Molecularinteractions such as hydrogen bonding are still not well-understood and are poorly predicted by the current theories.23

Therefore, the calculation of surface adhesion by contact anglemeasurements is indirect and an approximation in nature. Onthe other hand, the determination of adhesion is direct fromindentation measurements; different tips can be used todetermine the adhesion of a surface for various scenarios. Arecent study synthesized and functionalized poly(ethyleneglycol) microparticles as soft colloidal probe for adhesionmeasurements in aqueous media, which revealed adhesioncontributions due to acid−base, electrostatic, and hydrophobicinteractions.67

Figure 8b shows the plot of the extra load Pf versus the radiusof the contact area a and the fitting curve of thin film contactmechanics for polydopamine thin films. The effective elasticmodulus of polydopamine was determined using eq 11 to beabout 10 GPa. It has the same order of magnitude as the elasticmodulus of melanin (3−7 GPa), which has a similar chemicalstructure to polydopamine.68−70 This is the first time that theelasticity of polydopamine thin film is determined and isexpected to be valuable for its applications as a biocompatiblecoating material, which has been applied to function as atemplate for cell-patterning,32−35 to serve as a nanometer-thinad-layer for biomineralization or bone regeneration,36,37 and toimprint peptides, proteins and DNA/RNA for biosensing.38,39

Key results are summarized in Table 3 in comparison to the

available data in literature, demonstrating that the new methodand analysis allowed the direct measurements of both surfaceadhesion and elastic modulus of nanoscopic thin films.3.4. Technical Implications. It is worth discussing the

technical implications of the contact behavior of nanoscopicthin film in the integration of nanomaterials into functionaldevices. Delamination and cracking are two of the mostcommon issues in layered systems. While the delaminationoccurs at interfaces where adhesion plays the dominant role,the crack propagation in a film bonded to a substrate is a three-dimensional process in which a crack initiates at a flaw andadvances by channelling, as shown in Figure 9. The energyrelease rate Gss for a through-film crack subject to uniformloading stress σ and on a film of thickness h is

σ π α β= *Gh

Eg

2( , )ss

2

f (13)

where g(α,β) is a constant depending on the precise geometryand the elastic mismatch between the film and the substrate.Modeled by Beuth for a film on a flat mathematical half-space,this constant is a function of Dundurs parameters α and β.71

α

βμ μμ μ

=−+

=− − −− + −

* *

* *E EE E

v v

v v

(1 2 ) (1 2 )

2 (1 ) 2 (1 )

f sub

f sub

f sub sub f

f sub sub f (14)

where μ is the shear modulus of the material. The functiong(α,β) was computed by Beuth for most practical materialcombinations, where the value of β ranges between 0 and α/4,and is shown in Figure 9.71 The value of the function is low andasymptotic when the substrate is stiffer than the film (α < 0)but grows exponentially as the substrate gets softer. Thissuggests the driving force of channeling is independent to thesubstrate properties when a compliant film is bonded on a stiffsubstrate. However, if the same film is bonded on a substratesofter than the film, the energy release rate surges dramatically.In the presence of residue or applied stresses, the energy releaserate might well exceed the fracture toughness of the film,making it vulnerable to cracking and delamination. Thismechanic is well exhibited by polydopamine thin films, whichcrack during drying if coated on PDMS (α ≈ 1) but remainintact if coated on glass (α ≈ −0.9).64 In this respect, theelasticity of polydopamine serves as a design guideline for itssuccessful integration in applications, implying the substrateused should be stiffer than 10 GPa in order to avoiddeteriorations of the film.

4. CONCLUSIONIn summary, we have developed a new method for character-izing the microscopic contact behaviors of nanoscale stiff thinfilms by indenting with macroscopic hemispherical soft tip. Incontrast to the nanoindentation and buckling techniques forcharacterizing nanoscopic thin films, this method allows thesimultaneous determinations of both elastic modulus andsurface adhesion of thin films. The bending and stretching ofnanoscopic thin film in the microscopic contact areas wereanalyzed in the framework of JKR contact mechanics byincorporating the plate theory. The analysis established theextra stress required to compensate the contact resistancearising from the rigid thin coating film, which is used todetermine the effective elastic modulus of nanoscopic thinfilms. We validated this approach by applying it to 50 and 100nm gold thin films coated on elastomeric substrates having an

Table 3. Comparison of the Effective Elastic Modulus ofPolydopamine Thin Film with Literature Values and theWork of Adhesion between Polydopamine Thin Film andPDMS (Sylgard 170) with Theoretical Calculations UsingWu’s Method and van Oss’s Method

experimental comparison

Ef* (GPa) 10.1 ± 2.9 3−7 (melanin)Wsys(f) (mJ m

‑2) 39.0 ± 1.2 43.2 (Wu), 49.9 (van Oss)

Figure 9. Steady-state channelling of cracks in a thin film: schematicfor the process and value of function g(α,β) with respect to theparameters α and β (reproduced with permission from reference 71.Copyright 1992, Elsevier); the value for polydopamine coated on glass(○) and on PDMS (◊).

Langmuir Article


elastic modulus of 4−5 orders of magnitude lower than that ofgold. The effective elastic modulus of gold thin films wasdetermined to be close to the documented effective elasticmodulus of polycrystalline bulk gold of 98 GPa. It was foundthat the cracks on thin films had little effect on thedetermination of elasticity because the films were fully bondedand compliant to the substrates and the effect of cracks on thedeformation of the substrate was negligible.The advantages of this simple microindentation method for

characterizing nanoscale thin films were further demonstratedon self-polymerized dopamine thin films, a recently discovereduniversal coating material having a chemical structure ofcatecholamine mimicking the chemical composition of musseladhesive proteins. The elastic modulus of polydopamine thinfilms (70 nm thick) was determined to be 10 GPa, and itssurface adhesion to the PDMS tip was determined to be 39 mJm−2. These properties of polydopamine provide fundamentaldesign parameters for transferring polydopamine thin filmseffectively into practical applications. It showed our analysis andexperimental technique as a novel approach to quantify themicroscopic contact behaviors of thin films (<200 nm), whichhave been found difficult to measure by nanoindentation andare becoming increasingly important for innovative uses ofnanomaterials in such applications as touch-screen coatings,optical devices, stretchable electronics, and biosensors.

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This research was supported by the Natural Sciences andEngineering Research Council of Canada (NSERC). We aregrateful to Prof. T. Leung, Dr. L. Zhao, and Dr. N. Heinig forhelp in XRD measurements and to Prof. T. Tsui for advice onthin film characterizations.

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■ NOTE ADDED AFTER ASAP PUBLICATIONThis paper was published on the Web on May 31, 2012, beforethe author corrections were made. The corrected version wasreposted on June 5, 2012.

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“contact” of nanoscale stiff films

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