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1 This article was downloaded by: [Korea Advanced Institute of Science & Technology (KAIST)] On: 12 June 2014, At: 09:02 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Philosophical Magazine Letters Publication details, including instructions for authors and subscription information: Time-dependent adhesion of a polydimethylsiloxane (PDMS) elastomer film to a flat indenter tip characterized using a cohesive-zone law Nghia Trong Mai a, Seung Tae Choi a, Koo-Hyun Chung a, Seung Ryoon Lee b, Dong Kil Shin b & Youn Young Earmme b a School of Mechanical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan , Republic of Korea b Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon , Republic of Korea Published online: 14 Mar To cite this article: Nghia Trong Mai, Seung Tae Choi, Koo-Hyun Chung, Seung Ryoon Lee, Dong Kil Shin & Youn Young Earmme (2014) Time-dependent adhesion of a polydimethylsiloxane (PDMS) elastomer film to a flat indenter tip characterized using a cohesive-zone law, Philosophical Magazine Letters, 94:4, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,

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3 Philosophical Magazine Letters, 2014 Vol. 94, No. 4, , Time-dependent adhesion of a polydimethylsiloxane (PDMS) elastomer film to a flat indenter tip characterized using a cohesive-zone law Nghia Trong Mai a, Seung Tae Choi a *, Koo-Hyun Chung a, Seung Ryoon Lee b, Dong Kil Shin b and Youn Young Earmme b a School of Mechanical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan , Republic of Korea; b Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon , Republic of Korea (Received 24 June 2013; accepted 3 February 2014) The work of adhesion between a polydimethylsiloxane (PDMS) elastomer film and a flat diamond tip was measured by instrumented indentation. The results showed that the apparent work of adhesion between the tip and the PDMS film increases with increasing dwell time and retreating velocity; on the other hand, the indentation depth has no significant effect on adhesion. The indentation experiment was analysed with viscoelastic finite element simulations with rate-dependent cohesive elements, from which the time evolution of adhesion was quantitatively implemented into a rate-dependent cohesive-zone law. Keywords: elastomer; thin films; nanoindentation; finite element analysis; cohesive-zone law; rate-dependent adhesion 1. Introduction Contact adhesion of elastomers to other engineering materials, one of the key factors in soft lithography [1,2], shows time- and process-dependent characteristics, originating from viscoelastic and viscoplastic properties, surface roughness, evolution of chemical state, humidity, temperature, and so on [3 10]. Of these properties, the effects of crack propagation speed and temperature on adhesion have been extensively studied in conjunction with viscous behaviour of polymers [4,6]. Due to the viscoelastic nature of elastomers such as polydimethylsiloxane (PDMS), the work of adhesion is dependent on the rate of the debonding processes through the change of compliance and viscoelastic dissipation near the process zone, a process that has been ingeniously utilized in a transfer technique [2]. To gain an insight into the adhesive contact between flat surfaces, Kendall [11] was the first to develop an equilibrium theory of adhesion by analysing the work of *Corresponding author. stchoi@ulsan.ac.kr Dong Kil Shin is now at: School of Mechanical Engineering (Major of Mechanical Advanced Engineering), Yeungnam University, 280 Daehak-Ro, Gyeongsan, Gyeongbuk , Republic of Korea. This article was originally published with errors. This version has been corrected. Please see Erratum ( / ) Taylor & Francis

4 Philosophical Magazine Letters 243 adhesion of a flat punch to a planar surface. Recently, in accordance with the extensive applications of thin films, Choi et al. [12] extended Kendall s equilibrium theory of adhesion to analyse the adhesive contact between a flat punch and an elastic film on a rigid substrate and thus obtained a simple expression of the work of adhesion in terms of the shear modulus, Poisson s ratio, and thickness of the film, the radius of the flat punch, and the pull-off force at the instant of debonding. In conjunction with these theoretical developments, experimental investigations of adhesion have also been widely performed, typically using nanoindentation and atomic force microscopes. However, the work of adhesion of polymer films often exhibits time-dependent behaviour [3 10], which makes adhesive bonding and debonding phenomena much more complicated. In order to simulate the adhesive behaviour of a weak interface between solids, cohesive-zone models have been used effectively in finite element analysis (FEA) [13,14], in which the cohesive-zone laws relate the traction between the two adherends to the surface opening displacement (separation). Recently, several rate-dependent cohesive-zone models have been developed to take into account the time evolution of the apparent work of adhesion during the bonding and debonding processes [15 17]. Regardless of the physical origins of the rate-dependent behaviours, the cohesive-zone laws can be regarded as interfacial properties including all the complicated non-linear and inelastic characteristics. However, FEA using cohesive-zone models for the ratedependent work of adhesion has not been extensively explored due to the difficulties in measuring and implementing the time evolution of adhesion. In this paper, the time-dependent cohesive-zone law between a flat diamond tip and a PDMS film was quantitatively evaluated for the first time using flat-tip indentation experiments and the viscoelastic FEA. Nanoindentation was performed with a flat diamond tip on a PDMS film, of which the results were analysed with the extended Kendall s theory of adhesion [12]. The viscoelastic finite element simulation with cohesive elements was conducted to analyse the results of the indentation experiments. The viscoelastic FEA provided the cohesive-zone laws between the flat tip and PDMS film relying on the time-dependent variables of the indentation experiments. 2. Theoretical background Indentation with a flat-ended cylindrical tip on an elastic film is considered here. If the modulus of the film material is much smaller than those of the indenter tip and the substrate, as is usual for polymer films, the indenter and the substrate can be regarded as rigid bodies. Choi et al. [12] extended the Kendall s equilibrium theory of adhesion to analyse the adhesive contact between a flat tip and an elastic film on a rigid substrate, and obtained a simple expression of the work of adhesion, G as, G ¼ F 2 ð1 mþ 16pla 3 ½bðm; h=aþš 2 ; (1) where μ, ν, h, a, and F are the shear modulus, Poisson s ratio, the film thickness, the flat tip radius, and the applied force exerted by the flat tip, respectively. The relation in Equation (1) for the debonding of a flat tip from an elastic film differs from that for the debonding of a flat tip from a semi-infinite elastic solid only in the non-dimensional

5 244 N.T. Mai et al. multiplying factor, β(ν, h/a), which is plotted against h=a for several values of Poisson s ratio m in Figure 3 of Choi et al. [12]. It is worth noting that even though the energy release rate given in Equation (1) assumes that the film is elastic, it is also applicable to viscoelastic films if the viscoelastic losses are localized at the local debonding zone [6]. At the instant of the debonding of a tip from an elastic film, the equilibrium condition G cr = γ a makes it possible to measure the work of adhesion. 3. Flat indentation experiment A film of PDMS (Sylgard 184 Silicone Elastomer from Dow Corning Co., Midland, US) was used in the indentation experiment. A Sylgard 184 Silicone Elastomer is supplied as a two-part liquid component kit made up of the Base and the Curing Agent to be mixed in a 10:1 ratio by weight or volume. After the liquid components were mixed carefully, they were spin-coated at 3000 rpm for 60 s onto a 4-inch silicon (100) wafer with a thickness of 500 μm. The spin-coated PDMS film was then cured for 60 min at 85 C, and its thickness h was measured as 31 μm. Load-controlled indentation experiments on the PDMS films were performed using a Nano Indenter XP [18] (MTS Nano Instruments Innovation Center, Oak Ridge, TN) at room temperature (18 C), for which a flat-ended cylindrical diamond tip with a radius a = 20.4 μm was used. Choi et al. [19] developed a modified-creep experiment with Nano Indenter XP, in which the head dynamics of the Nano Indenter XP was taken into account. In order to measure the work of adhesion between a PDMS film and a flat tip, the same procedure as the modified-creep experiment was adopted in this study, of which the details are well summarized by Choi et al. [19] but not reproduced here for compactness. The indentation experiment was composed of three steps: (1) loading step, (2) holding step, and (3) unloading step. In the loading step, the raw load was controlled to make the displacement of the flat tip into the specimen surface increase to an indentation depth d 0 with a velocity v l = 300 nm/s. In the holding step, the raw load was held constant for a dwell time t d. Finally, in the unloading step, the raw load was decreased, resulting in a retreating velocity v u of the flat tip, until the flat tip is completely debonded from the PDMS film. 4. FEA with time-dependent cohesive-zone laws The flat indentation experiment described above was analysed with finite element simulation using cohesive elements along the interface between the tip and the PDMS film, of which the traction separation law is given as [13 16]. T n ¼r max exp 1 a D (! "!# n Dn exp D2 t d n d n d 2 þ 1 q r 1 1 exp D2 t t d 2 r D ) n d t n (2) d D n þ 1 n ; dt d n d n Dt T t ¼ 2r max q þ r q D n exp D! n exp D2 t d D t d t d t r 1 d n d n d 2 þ 1 t : (3) dt d t t

6 Philosophical Magazine Letters 245 Here, T n, T t, D n, and D t are the normal traction, tangential traction, normal separation, and tangential separation, respectively. r max, d n, and d t are the cohesive strength, characteristic opening displacement, and characteristic shearing displacement, respectively. The last terms in Equations (2) and (3) represent an additional viscous dissipation introduced to regularize instabilities, which are likely to occur at the first debonding of weak interfaces, and thus, 1 n and 1 t are fictitious viscous parameters used to avoid instabilities but not to model any physical energy dissipation [14]. The dimensionless parameters q and r were chosen to be 1 and 0, respectively, for simplicity. Since the adhesive contact between the flat tip and PDMS film is for the most part normal but hardly tangential in the flat indentation experiment, Equations (2) and (3) may be further simplified by assuming the characteristic shearing displacement d t to be infinity, yielding a tangential traction that is always zero. In order to make the cohesive-zone law given in Equations (2) and (3) rate dependent, it is assumed that the dimensionless parameter a depends on the separation rate D 0 n [15,16]: a ¼ a 0 þð1 a 0 Þ exp j D0 n d 0 ; (4) 0 where a 0, j, and d 0 0 are dimensionless parameters controlling the dependence of the cohesive-zone traction on the separation rate. Moreover, it is worth noting that during the holding step, as can be seen from Figure 1, even though the applied force gradually decreases, the indentation depth gradually increases. Therefore, the actual contact area at nanoscale between the flat tip and the PDMS film may increase, causing the increase of the cohesive strength between the flat tip and the PDMS film. Consequently, in order to take into account the effect of the dwell time, we propose that the parameter σ max can be expressed as a function of contact time t c : Figure 1. (colour online) Applied force vs. indentation depth curves of the flat indentation experiment on a PDMS film with a thickness of 31 μm. The minimum values of the applied force correspond to the pull-off forces.

7 246 N.T. Mai et al. r max ¼ r 0 þ r c 1 exp t c t 0 ; (5) where r 0 and r c are the initial and additional cohesive strengths, respectively, and t 0 is a reference time constant. The cohesive-zone law of Equations (2) and (3) combined with Equations (4) and (5) can be used to simulate the effects of the retreating velocity v u in the unloading step and dwell time t d on the pull-off force and thus on the work of adhesion between the flat diamond tip and the PDMS film. It is worth noting that the retreating velocity v u and dwell time t d may be considered to be the gross quantities of the separation rate D 0 n and the contact time t c, respectively, experienced by each of the cohesive elements. The commercial software ABAQUS Ver [20] was used for the FEA of the flat indentation experiment, in which the PDMS film was assumed to be viscoelastic, while the flat diamond tip and the Si substrate to be rigid. The viscoelastic properties of the PDMS film measured by Choi et al. [19] were used in the FEA. The interface between the tip and PDMS film was modelled using cohesive elements, to which the rate-dependent traction separation law described with Equations (2) (5) was implemented into the ABAQUS user subroutine UEL [14,20]. 5. Results and discussion The flat indentation experiment was performed with various indentation depths ( nm), in which the parameters t d and v u were fixed at 300 s and 500 nm/s, respectively. It was observed that the indentation depth has no significant influence on the measured pull-off force and thus work of adhesion. Similar results were also confirmed by the FEA using the rate-dependent cohesive-zone laws. For the indentation depth of nm, the average strain defined as ɛ 0 = d 0 /h becomes 2.26% ɛ %. It can be inferred that at least in this range of average strain, viscoplastic deformation in the PDMS film may not prevail and the absolute value of the average strain has little effect on adhesion. All further experiments and FEA were therefore performed with a fixed indentation depth d 0 of 1000 nm. Flat indentation experiments were performed on the PDMS film with various retreating velocities v u = nm/s with the dwell time fixed at t d = 300 s; the resulting applied force vs. depth curves are plotted in Figure 1. It was observed that during the dwell time, the indentation depth and the applied force gradually change due to the viscoelastic behaviour of the PDMS film, as explained in detail by Choi et al. [19]. By analysing the linear loading segment (i.e. rising segment) of the flat indentation curve, in which the elastic behaviour of the PDMS film prevails over the viscoelastic behaviour, the shear modulus μ(0) of the PDMS film was determined to be kpa, assuming the Poisson s ratio as 0.48 [19]. During unloading, debonding takes place when the energy for debonding is sufficient to overcome the material resistance, which largely comes from the adhesion energy between the diamond tip and the PDMS film. The pull-off force at the moment of debonding was taken as the minimum force of the force depth curve, as shown in Figure 1. The above-mentioned flat indentation experiments were analysed with viscoelastic axisymmetric finite element simulations, of which the applied force vs. indentation depth curves are shown in Figure 2. In the FEA, the head structure of the Nano

8 Philosophical Magazine Letters 247 Figure 2. (colour online) Applied force vs. indentation depth curves obtained by viscoelastic FEA using rate-dependent cohesive-zone laws. Indenter XP as illustrated in Figure 1b of Choi et al. [1] was modelled with a flat cylindrical tip connected to two virtual springs having the same configuration and spring constants as the support spring and the load frame of the Nano Indenter XP. This configuration can successfully simulate the modified-creep experiment performed in this study. Especially, it should be noted in Figure 1 that during the holding step, both of the applied force and the indentation depth gradually changed. In a similar way, the applied force-indentation depth curves obtained by the FEA show the same behaviour in the holding step as shown in Figure 2. The main difference between the experimental and numerical force depth curves is the shape of the unloading curves as shown in Figures 1 and 2, respectively. It was observed in the indentation experiment that viscoelastic response of the PDMS film depends on the retreating velocity of the flat tip in the unloading step, which alters the unloading stiffness, i.e. the slope of the force depth curves (Figure 1). On the other hand, the viscoelastic properties of the PDMS film measured by Choi et al. [19] and used in the FEA may not effectively account for the viscoelastic response during the unloading step, because the shortest time constant of the measured relaxation modulus of the PDMS film is s. In other words, in the FEA, the behaviour of the PDMS film may not fully incorporate the viscoelastic nature of the PDMS film for time periods shorter than or comparable to the shortest time constant. Therefore, during the loading (3.3 s) and unloading steps ( s), the PDMS film may respond nearly elastically, resulting that the slopes of the force displacement curves during the unloading step obtained from the FEA (Figure 2) are almost constant and independent of the retreating velocity of the flat tip. However, it is worth noting that the measured pull-off force and thus work of adhesion strongly depend on the debonding velocity of the flat tip from the PDMS film, i.e. crack propagation speed, as described by several researchers [3,4,6], but not on the stiffness change of the PDMS film. Usually, critical energy release rate during crack propagation in viscoelastic solids depends on the crack propagation speed, since viscoelastic loss at the crack tip strongly depends on the crack propagation speed [3,4,6]. This dependence

9 248 N.T. Mai et al. Table 1. Numerical parameter values for the rate-dependent cohesive-zone law between a PDMS film and a flat diamond tip. Parameters σ 0 σ c d n t 0 a 0 j d 0 0 Values MPa MPa 20 nm 1000 s nm/s of pull-off force and thus work of adhesion on the crack propagation speed can be implemented into the cohesive-zone laws between the tip and PDMS film. In order to fit the experimental pull-off force data to the FEA results, the parameters used in the cohesive-zone law given in Equations (2) (5) were adjusted by trial and error. The resulting numerical values are listed in Table 1. The pull-off forces determined by the experiments and FEA are plotted in Figure 3 as a function of the retreating velocity v u in the unloading step. The measured pull-off forces were obtained at 10 different points for each unloading velocity and then used to construct the box plot presented in Figure 3. It is clear that the pull-off force is an increasing function of the retreating velocity v u. From Equation (1), the apparent work of adhesion can be calculated as γ a = G cr, as shown in Figure 3. In the calculation of the apparent work of adhesion, the non-dimensional parameter bðm ¼ 0:48; h=a ¼ 1:522Þ ¼ was used [12]. Flat indentation on the PDMS film was also performed for various dwell times using a fixed v u = 500 nm/s; the measured pull-off force is plotted in Figure 4. The pulloff force is also shown to increase with increasing dwell time, a trend different from that of SU-8 [12], for which the dwell time does not affect the work of adhesion. There are several physical phenomena known as the origin of the dwell time s effect on adhesion: surface bloom [5], surface roughness [7,10], chemical reaction [9], etc. Among them, change of surface roughness at nanoscale may increase the actual contact area between the flat tip and the PDMS film, mainly causing the increase of the cohesive strength between the flat tip and the PDMS film. Therefore, the effect of the dwell time on adhesion (increasing adhesion with increasing dwell time) was implemented into the Figure 3. (colour online) The pull-off force and apparent work of adhesion as a function of the retreating velocity obtained by flat indentation experiments and viscoelastic FEA. Here, the dwell time was fixed as t d = 300 s.

10 Philosophical Magazine Letters 249 Figure 4. (colour online) The pull-off force and apparent work of adhesion as a function of the dwell time, as obtained by the flat indentation experiments and viscoelastic FEA. Here, the retreating velocity was fixed to v u = 500 nm/s. cohesive-zone laws through the cohesive strength given in Equation (5). The numerical parameter values listed in Table 1 were set by trial and error to fit the results of FEA to the measured work of adhesion dependent on dwell time, as shown in Figure 4. It is worth noting that the cohesive-zone law in Equations (2) (5) together with the numerical parameter values in Table 1 can be used to model the time-dependent adhesive bonding and debonding processes between diamond and PDMS materials in the appropriate separation rate and contact time ranges. Furthermore, since the time dependence of adhesion can be attributed to the PDMS film rather than the diamond tip, the current results can be qualitatively applied to the adhesive contact of PDMS materials to other hard materials. For example, one could deposit a metal on top of the flat diamond tip to study the adhesive contact between the metal and PDMS film. It is well known that the detailed shape of the cohesive-zone law is not important; rather, its area provides the adhesion energy, which can be obtained by integrating the cohesive traction with respect to the separation according to c a ¼ Z 1 0 T n ðd n ÞdD n ¼ e a 2 r maxd n ; (6) where the separation rate D 0 n is assumed to be constant. Equation (6) represents the dependence of the adhesion energy on the separation rate D 0 n and the contact time t c through the parameters a and r max given in Equations (4) and (5), respectively. 6. Conclusion In conclusion, indentation experiments with a flat diamond tip with a radius of 20.4 μm were performed on a 31 μm thick PDMS film. The indentation results showed that the work of adhesion between the tip and the PDMS film is a function increasing with dwell time and retreating velocity of the flat tip in the unloading step and that the work

11 250 N.T. Mai et al. of adhesion varies from approximately mj/m 2 for dwell times between 100 and 1000 s and retreating velocities between 100 and 700 nm/s. Indentation depths between 700 and 1300 nm have no significant effect on the work of adhesion. Flat indentation experiments were analysed with viscoelastic finite element simulation, in which rate-dependent cohesive-zone laws were used to simulate the time evolution of interface adhesion between the tip and PDMS film. The rate-dependent cohesive-zone laws between the tip and PDMS film were obtained quantitatively by viscoelastic FEA. The methodology developed in this study can be utilized to characterize the rate-dependent adhesion properties of many combinations of tip and polymeric film materials. Acknowledgements This work was supported by the 2012 Research Fund of University of Ulsan. References [1] M. Brehmer, L. Conrad and L. Funk, J. Dispersion Sci. Technol. 24 (2003) p.291. [2] M.A. Meitl, Z.T. Zhu, V. Kumar, K.J. Lee, X. Feng, Y.Y. Huang, I. Adesida, R.G. Nuzzo and J.A. Rogers, Nat. Mater. 5 (2006) p.33. [3] A.N. Gent and J. Schultz, J. Adhes. 3 (1972) p.281. [4] E.H. Andrews and A.J. Kinloch, Proc. R. Soc. London, Ser. A 332 (1973) p.385. [5] A.D. Roberts and A.B. Othman, Wear 42 (1977) p.119. [6] D. Maugis and M. Barquins, J. Phys. D: Appl. Phys. 11 (1978) p [7] C. Creton and H. Lakrout, J. Polym. Sci., Part B: Polym. Phys. 38 (2000) p.965. [8] K. Vorvolakos and M.K. Chaudhury, Langmuir 19 (2003) p [9] D. Bodas and C. Khan-Malek, Sens. Actuators, B 123 (2007) p.368. [10] E.P. Chan, E.J. Smith, R.C. Hayward and A.J. Crosby, Adv. Mater. 20 (2008) p.711. [11] K. Kendall, J. Phys. D: Appl. Phys. 4 (1971) p [12] S.T. Choi, S.R. Lee and Y.Y. Earmme, J. Phys. D: Appl. Phys. 41 (2008) p [13] X.P. Xu, A. Needleman, J. Mech. Phys. Solids 42 (1994) p [14] Y.F. Gao and A.F. Bower, Modell. Simul. Mater. Sci. Eng. 12 (2004) p.453. [15] A. Corigliano, S. Mariani and A. Pandolfi, Compos. Struct. 61 (2003) p.39. [16] A. Corigliano, S. Mariani and A. Pandolfi, Compos. Sci. Technol. 66 (2006) p.766. [17] C. Xu, T. Siegmund and K. Ramani, Int. J. Adhes. Adhes. 23 (2003) p.9. [18] The Nano Indenter XP User s Manual Ver. 16, MTS Systems Corporation, [19] S.T. Choi, S.J. Jeong and Y.Y. Earmme, Scr. Mater. 58 (2008) p.199. [20] ABAQUS User s Manual, Ver. 6.12, Dassault Systèmes Simulia Corp., Providence, RI, USA.