Mechanics Modelling of Hierarchical Wrinkle Structures from

Dec 3, 2018 - Three-dimensional (3D) hierarchical wrinkles can be generated on pre-strained thermoplastic substrates by sequential cycles of skin laye...
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Mechanics Modeling of Hierarchical Wrinkle Structures from the Sequential Release of Prestrain Yeguang Xue,†,‡,° Won-Kyu Lee,§,∇,° Jianghong Yuan,# Teri W. Odom,*,§,∥ and Yonggang Huang*,†,‡,⊥ Department of Civil and Environmental Engineering, ‡Department of Mechanical Engineering, §Department of Materials Science and Engineering, ∥Department of Chemistry, and ⊥Center for Bio-Integrated Electronics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States # School of Mechanics and Engineering, Southwest Jiaotong University, No. 111 First Section of Second Ring Road, Chengdu, Sichuan 610031, China Langmuir Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 12/17/18. For personal use only.

†

S Supporting Information *

ABSTRACT: Three-dimensional (3D) hierarchical wrinkles can be generated on prestrained thermoplastic substrates by sequential cycles of skin layer growth followed by the release of prestrain. However, no mechanics models have explained the formation of multigenerational nanostructures using this nanofabrication process. This article describes an analytical model that can represent multiscale wrinkles with arbitrary numbers of generations. Structural features including wrinkle wavelengths and amplitudes on the nanoscale that are predicted by minimizing the total deformation energy of the system. The calculated wavelengths in each generation are in good agreement with experiment. Our mathematical approach provides design principles for achieving multigenerational hierarchical structures.

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INTRODUCTION The formation of three-dimensional (3D) surface patterns, especially hierarchical structures consisting of multigenerational features across different length scales, enables many applications such as antibiofouling,1 tunable wettability,2,3 drag reduction,4 reversible dry adhesion,5 and controlled light absorption.6 Realizing 3D surface morphologies, however, typically involves complex top-down techniques such as multistep photolithography and imprinting7 that cannot easily produce multiscale features over large areas (>cm2). Wrinkle patterns generated by the compressive buckling of stiff skin layers on prestrained substrates provide an approach for the spontaneous formation of out-of-plane structural hierarchical materials.8−15 In the low-strain regime, the wrinkle wavelength is linearly proportional to the thickness of the skin layer and depends on the modulus ratio of the skin and substrate.12,13,16 The resulting wavelength (λ), defined here as the periodicity of the wavy features, can be tuned over a wide range, from 100 nm to 100 μm.13 The wrinkled topologies can be adjusted by further mechanics loading (e.g., stretching or compression of the substrate)13,16 such that the surface morphology can be dynamically tuned. We recently reported a memory-based nanowrinkling approach in which multiple cycles of skin layer formation followed by the release of prestrain in the thermoplastic substrates achieved hierarchical textures.17,18 During the sequential wrinkling process, generational nanostructures with larger λ values were produced without changing the © XXXX American Chemical Society

topography of the underlying smaller wrinkles, which preserves the structural hierarchy in 3D. This bottom-up approach is distinct from one-step buckling procedures because the feature orientation and λ of each wrinkle generation can be independently controlled by changing the directional strain and thickness of the skin layers, respectively.19 Robust surface functionalities, such as lotus-type superhydrophobicity18 and antibiofouling effects,20 have been demonstrated on hierarchical wrinkles. Analytical models have been developed to study the wrinkling of stiff, thin skin layers on compliant substrates.8,12,13,16,21 Although the models quantitively reproduce λ and amplitude observed in experiments, these mechanics models are applicable only to first-generation (G1) wrinkling formed by one-step buckling. Suitable mechanics models have not yet been established to explain the behavior of multigenerational wrinkling [e.g., second generation (G2) and third generation (G3) wrinkling]. Here, we report a mechanics model for the sequential wrinkling process that produces outof-plane structural hierarchy. We mathematically derived G1 and G2 structural features and then generalized the analytical expressions to arbitrary generations. The predicted λ matched well with experimental data. Importantly, design guidelines on Received: October 17, 2018 Revised: November 30, 2018 Published: December 3, 2018 A

DOI: 10.1021/acs.langmuir.8b03498 Langmuir XXXX, XXX, XXX−XXX

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Figure 1. Schematic illustration of the sequential approach to forming hierarchical wrinkles (G1, G2, and G3 wrinkles). In each generation, CHF3 RIE treatment forms a thin skin layer on the structure. The controlled release of prestrain in the polystyrene (PS) substrate produces the hierarchical wrinkling morphology.

and zero shear stress on its top surface8 (Supporting Information, eqs S9−S11). Minimization of the total energy of the system UG1 = U̅ 1mL0 + U̅ 1bL0 + U̅ sL* with respect to λ10 and A1 (∂UG1/∂λ10 = ∂UG1/∂A1 = 0) gives both λ10 and A1 (Supporting Information, eqs S12 and S13). In the state of prestrain release of εG1, the actual wavelength (as measured in experiments) can be reduced to

forming hierarchical wrinkles are now established on the basis of the developed model.

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RESULTS AND DISCUSSION For sequential wrinkling,17 prestrained thermoplastic polystyrene (PS) sheets were used as the substrates, and CHF3 plasma treatment formed thin fluoropolymer skin layers. Figure 1 shows a scheme of the sequential wrinkling processes used to form multiscale, hierarchical structures consisting of G1, G2, and G3 features. The first skin layer (thickness h1 and length L0) was first formed on flat, prestrained PS (initial length L* at its stress-free state and prestretched to length L0). The release of prestrain by εG1 [from length L0 to length L0(1 − εG1)] resulted in G1 wrinkling. In the next step, the second skin layer [thickness h2 and length L0(1 − εG1)] conformally formed on G1 features, and further release of prestrain to εG2 [from length L0(1 − εG1) to length L0(1 − εG2)] generated G2 wrinkling. Repeating this process produced higher-generation wrinkles (e.g., G3 wrinkles corresponding to thickness h3 and the release of prestrain to εG3) without deforming smaller G1 and G2 features, which highlights the robust memory effects of the system.17 Analytical models for G1 wrinkling have already been developed in previous work.8,12,13,16 The thin skin layer (G1 layer) is modeled as a beam, and after strain release, out-ofplane displacement w 1 takes a sinusoidal form,

( x), where A

[w1(x)]G1 = A1 cos

2π λ10

1

ij E ̅ yz λG1 = (1 − εG1)λ10 = 2πh1(1 − εG1)jjj f zzz j 3Es̅ z k {

1/3

(1)

where E̅ f and E̅ s are the plane-strain modulus of the skin layer and the substrate, respectively, and h1 is the thickness of the G1 skin layer. The critical strain to be released to form G1 wrinkles (εG1)cr is also obtained from the minimization (Supporting Information, eq S14). After forming the second skin layer (G2 skin) with thickness h2, further release of prestrain by εG2 − εG1 [i.e., length of the substrate reduced from L0(1 − εG1) to L0(1 − εG2)] gives rise to G2 wrinkling. Similar to G1 wrinkling, the displacement in the G2 skin layer also takes a sinusoidal form,

( x) where A

[w2(x)]G2 = A 2 cos

2π λ 20

2

is the amplitude and λ20

is the wavelength of G2 wrinkling in the original x−z coordinate system. Importantly, the actual wavelength in the stress-free state of the G2 skin layer is λ20(1 − εG1). The projected length of the G2 skin layer in the horizontal direction changes from L0(1 − εG1) to L0(1 − εG2), which yields to the effective release of prestrain (εG2 − εG1)/(1 − εG1). As we assumed in G1 wrinkling, any interfacial shear is neglected, and hence the analytical model for wrinkling of the G2 skin layer can be derived in a manner similar to that for G2 wrinkling. In detail, the membrane energy and bending energy per unit length for the G2 skin U̅ 2m and U̅ 2b can be obtained by replacing h1, A1, λ10, and εG1 with h2, A2, λ20(1 − εG1), and (εG2 − εG1)/(1 − εG1), respectively (Supporting Information, eqs S15 and S16). For the G1 skin layer, total displacement from its undeformed state includes deformation due to both G1 and

is the amplitude and λ10

is the wavelength in the original undeformed x−z coordinate system. Using the condition that membrane strain is constant along the skin layer,8,13,16 together with the boundary conditions corresponding to the release of prestrain εG1, the in-plane displacement u1 can be obtained (Supporting Information, eqs S1−S5). The membrane energy per unit length U̅ 1m can then calculated on the basis of displacement fields w1 and u1, which is also constant along the G1 skin layer (Supporting Information, eqs S6 and S7). The bending energy per unit length U̅ 1b is obtained by averaging over one wrinkle wavelength λ10 (Supporting Information, eq S8). The substrate energy per unit length U̅ s (in the stress-free state of the substrate) is obtained by modeling the substrate as a semiinfinite elastic solid subject to prescribed normal displacement

( x) + A cos( x)

G2 wrinkling, i.e., [w1(x)]G2 = A1cos

2π λ10

2

2π λ 20

For this out-of-plane displacement, the in-plane displacement B

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of G1, G2, and G3 wrinkles were λexperiment = 220 nm, λexperiment G1 G2 experiment = 1.0 μm, and λG3 = 12 μm, respectively. We determined the modulus ratio E̅ f/E̅ s = 47 by calculating the slope of the linear fit for the G1 wavelength. By inserting the E̅ f/E̅ s value into eq 2, we found the wavelength of G2 wrinkles (λmodeling = G2 1 μm), which agrees well with experiment (λexperiment = 1.0 G2 μm). Equation 3 gives the wavelength of G3 wrinkles (λmodeling G3 = 10 μm), which is also similar to experiment (λexperiment = 12 G3 μm). Notably, the wavelengths predicted by the model are sensitive to the amount of prestrain release. For example, the predicted wavelength for G3 wrinkling would be λmodeling = 12 G3 μm, in perfect agreement with the experiments, if εG3 were changed slightly from 0.9 to 0.88. Figure 2 shows the

u1 can be obtained following the same approach as for G1 wrinkling (Supporting Information, eqs S17−S21) and similar to the constant membrane energy per unit length (Supporting Information, eqs S22 and S23). In G2 wrinkling, the periodicity of displacement for G1 skin depends on the ratio of λ20/λ10 and exists only when the ratio is a rational number. We calculated the bending energy of the G1 skin layer per unit length U̅ 1b by averaging over length nλ20 and taking the limit n → ∞ (Supporting Information, eq S24). The substrate energy per unit length U̅ s was obtained for prescribed out-of-plane displacement (as we derived the analytical expression for the G1 skin layer based on continuity) with zero shear stress on the top surface (Supporting Information, eqs S25−S27). The total energy UG2 consists of the membrane and bending energy of G1 and G2 skin layers and substrate energy (UG2 = U̅ 1mL0 + U̅ 1bL0 + U̅ 2mL0 + U̅ 2bL0 + U̅ sL*). After wrinkling, we defined the deformed skin layer with two different lengths: (1) The horizontal length by projecting the curve onto the flat surface and (2) the true length of the wrinkled skin. The horizontal length with strain relief can be expressed as L0(1 − εG1), and the true length is ca. L0 because the G2 skin layer is conformal on the G1 wrinkles and the length of the G1 skin layer barely changes during wrinkling due to its small membrane strain (ε1m ≪ εG1). The minimization of UG2 (∂UG2/∂λ20 = ∂UG2/∂A2 = 0) gives λ20 and A2 (Supporting Information, eqs S28 and S29). The wavelength of G2 wrinkling is then Ä 1/3Å

ij E̅ yz λG2 = (1 − εG2)λ 20 = 2π (1 − εG2)jjjj f zzzz k 3Es̅ {

ÑÉÑ1/3 ÅÅ ÑÑ h23 ÅÅh 3 + Ñ ÅÅ 1 4Ñ ÅÅ (1 − εG1) ÑÑÑÑÖ ÅÇ

Figure 2. Comparison of analytical model and experimental results for the G2 wrinkling wavelength. Here for the CHF3 plasma-treated PS system, the G1 skin layer thickness is fixed as h1 = 10 nm and the G2 skin layer thickness h2 ranges from 40 to 120 nm. The release of prestrain in the experiment of the G1 and G2 wrinkling process is seen in εG1 ≈ 0.4 and εG2 ≈ 0.6, respectively.

(2)

The critical release of prestrain (εG2 − εG1)cr for the onset of G2 wrinkling can also be obtained from the energy minimization approach (Supporting Information, eq S30). After a third skin layer (G3 skin) with thickness h3 is formed, further release of the prestrain by εG3 − εG2 leads to G3 wrinkling. The wavelength can be calculated analytically λG3 = (1 − εG3)λ30

ÑÉÑ1/3 ÅÅ ÑÑ h33 h23 ÅÅ 3 Ñ + ÅÅh1 + ÑÑ 4 4Ñ ÅÅ (1 ) (1 ) − ε − ε ÑÖ ÅÇ G1 G2 Ñ

experimental data of G2 wavelengths with varying h2 from 40 nm to 120 nm (with the same h1 = 10 nm, and εG1 ≈ 0.4 and εG2 ≈ 0.6).17 Using the same modulus ratio of E̅ f/E̅ s = 47, the wavelength predicted by the model agrees very well with the experiments. Our analytical model provides important insight about the conditions for forming multigenerational wrinkle patterns (Figure 3). The structural hierarchy, which is equivalent to the higher-generation wrinkle structures, requires two conditions. First, the release of prestrain needs to exceed its critical value (e.g., eq S14 for G1 and eq S30 for G2). This condition is easily satisfied by applying a larger prestrain. In our system, the critical release of prestrain for G1 is only (εG1)cr = 4.0%, and the critical strain for forming G2 is even smaller. For a representative thickness ratio h2/h1 = 3, (εG2 − εG1)cr = 1.6% for εG1 = 0.3, and (εG2 − εG1)cr = 1.9% for εG1 = 0.1. Second, the wavelengths between different generations of wrinkling (e.g., λ10 and λ20) should be different enough to display a clear structural hierarchy. Starting from the same G1 wrinkle pattern (Figure 3a, modulus ratio E̅ f/E̅ s = 47, εG1 = 0.2), Figure 3b−d shows different G2 wrinkles by applying the same amount of strain εG2 = 0.3 but with different thickness ratios h2/h1 = 1.5, 3, and 5. For small thickness ratios (e.g., h2/h1 = 1.5), the G2 wrinkle pattern does not show a clear hierarchy (Figure 3b) because of the small wavelength ratio between generations (λ20/λ10 = 2.1). With increased thickness ratios h2/h1 = 3 and h2/h1 = 5, the wavelength ratio between generations increases to λ20/λ10 = 4.1 and λ20/λ10 = 6.7, respectively (Figure 3c,d). As the wavelength ratio increased, the local geometries of G2

Ä 1/3Å

ij E ̅ yz = 2π(1 − εG3)jjjj f zzzz k 3Es̅ {

(3)

The above formula can be generalized to the kth skin layer (Gk skin layer) with thickness hk under the release of prestrain by εGk − εG(k−1), i.e., 1/3l

λGk

ji E ̅ zy = 2π(1 − εGk)jjj f zzz j 3Es̅ z k {

o o o mh13 + o o o n

k

∑ j=2

|1/3 o o o } o [1 − εG(j − 1)]4 o o ~ hj3

(4)

From analytical models in eqs 1, 2, 3, and 4, we found that all multigenerational wrinkles were linearly proportional to (E̅ f/ E̅ s)1/3, which indicates that the ratio of wavelengths between different generations is independent on modulus ratio E̅ f/E̅ s and depends only on the skin thickness and the release of prestrain. An accurate prediction of wavelengths across different length scales provides important design guidelines for fabricating the structural hierarchy necessary for different applications.20 We now compare this model with hierarchical wrinkle structures generated with three sequential cycles17 and skin layers with h1 = 20 nm, h2 = 220 nm, and h3 = 1.8 μm, where the corresponding total release of prestrain for each generation was εG1 ≈ 0.3, εG2 ≈ 0.6, and εG3 ≈ 0.9. The measured wavelengths C

DOI: 10.1021/acs.langmuir.8b03498 Langmuir XXXX, XXX, XXX−XXX

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Figure 4. Design diagram of the thickness ratio between two adjacent generations hk/hk−1 and effective release of prestrain for the G(k − 1) step to achieve clear structural hierarchy for the representative critical ratio of the wavelengths ξcr = 3, 5, 10.

exceed the critical value ξcr. Therefore, the thickness ratio needs to satisfy h2 > h1

3

(ξcr 3 − 1)(1 − εG1)4 ≈ ξcr(1 − εG1)4/3

(5)

More generally, for k ≥ 3, for the wavelength ratio of G(k − 1) and G(k) wrinkling to be larger than the critical value ξcr for the original x−z coordinate system (which is the same in the current configuration), the thickness ratio must satisfy

Figure 3. Hierarchical wrinkle patterns predicted by the analytical model. (a) G1 wrinkle pattern with modulus ratio Ef/Es = 47 and εG1 = 0.2. (b−d) G2 wrinkle patterns from the same G1 wrinkle pattern (a) by applying the same amount of strain εG2 = 0.3 but with different values of the thickness ratio h2/h1 = 1.5, 3, and 5. (e−g) G3 wrinkle patterns from the same G2 wrinkle pattern (c) by applying the same amount of strain εG3 = 0.4 but with different values of the thickness ratio h3/h2 = 1.5, 3, and 5. With increasing values of the thickness ratio, the structural hierarchy becomes clearer. Conditions of h3/h2 = 3 and h3/h2 = 5 resulted in λ30/λ20 = 3.6 and λ30/λ20 = 6.0, respectively, whereas h3/h2 = 1.5 induced only λ30/λ20 = 1.9.

hk > hk − 1

3

(ξcr

3

ÄÅ É ÄÅ É ÅÅ 1 − εG(k − 1) ÑÑÑ4 ÅÅ 1 − εG(k − 1) ÑÑÑ4/3 ÅÅ ÑÑ ÅÅ ÑÑ − 1)ÅÅ Ñ ≈ ξcrÅÅ Ñ ÅÅ 1 − εG(k − 2) ÑÑÑ ÅÅ 1 − εG(k − 2) ÑÑÑ ÅÇ ÑÖ ÅÇ ÑÖ

(6)

Using this analytical expression, the effective release of 1 − εG(k − 1) prestrain in the G(k − 1) step can be defined as , 1 − εG(k − 2)

wrinkles became more regular with obvious G1 + G2 structural hierarchy (Figure 3c,d). Also, our model can be used to predict additional structural hierarchies of G1 + G2 + G3 wrinkle features. Figure 3e−g shows how different G3 wrinkles could form from the same G1 + G2 wrinkle pattern (Figure 3c, h2/h1 = 3) by applying the same amount of strain εG3 = 0.4 but with different thickness ratios of h3 to h2, i.e., h3/h2 = 1.5, 3, and 5. Similar to the G1 + G2 cases, G1 + G2 + G3 wrinkle patterns with increased thickness ratios have larger wavelength ratios between generations, giving rise to more distinct structural hierarchy. In addition, our model can also identify experimental conditions for achieving multigenerational nanostructures from sequential wrinkling. Here, we set the design diagram of hk/ hk−1 versus the effective release of prestrain to form distinct structural hierarchies by G(k − 1) wrinkling (Figure 4). For simplicity, we define the critical ratio of the wavelengths between generations (ξcr > 1) as the new design parameter and found that ξcr should be larger than 3. The ratio of G1 and G2 wrinkling wavelengths at the undeformed, original x−z coordinate system for the G1 skin layer (λ20/λ10, the same as the wavelength ratio in the deformed configuration) must

which is the ratio of the total length of the substrate after and before the release of prestrain in the G(k − 1) wrinkling process. From the diagram of hk/hk−1 versus the effective release of prestrain for different ξcr values, we can predict the resulting geometries of hierarchical wrinkles under the given processing conditions.

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CONCLUSIONS We established an analytical model to explain the hierarchical wrinkling process with cyclic skin formation and strain relief. The resulting wrinkle wavelength from each cycle can be predicted by the model, and the calculated values agree well with the experimental results. Our approach revealed that the design of structural hierarchy consisting of multigenerational wavelengths and amplitudes depends only on the skin thickness ratios and the release of prestrain. Considering that our mathematical tool provides a convenient way to predict not only the quantitative structural parameters but also the experimental conditions for the desired hierarchy, sequential nanowrinkling can now be generalizable to the fabrication of 3D nanostructures. D

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(9) Chapman, C. T.; Paci, J. T.; Lee, W. K.; Engel, C. J.; Odom, T. W.; Schatz, G. C. Interfacial Effects on Nanoscale Wrinkling in GoldCovered Polystyrene. ACS Appl. Mater. Interfaces 2016, 8 (37), 24339−24344. (10) Paci, J. T.; Chapman, C. T.; Lee, W. K.; Odom, T. W.; Schatz, G. C. Wrinkles in Polytetrafluoroethylene on Polystyrene: Persistence Lengths and the Effect of Nanoinclusions. ACS Appl. Mater. Interfaces 2017, 9 (10), 9079−9088. (11) Khang, D. Y.; Jiang, H. Q.; Huang, Y.; Rogers, J. A. A stretchable form of single-crystal silicon for high-performance electronics on rubber substrates. Science 2006, 311 (5758), 208−212. (12) Jiang, H. Q.; Khang, D. Y.; Song, J. Z.; Sun, Y. G.; Huang, Y. G.; Rogers, J. A. Finite deformation mechanics in buckled thin films on compliant supports. Proc. Natl. Acad. Sci. U. S. A. 2007, 104 (40), 15607−15612. (13) Song, J.; Jiang, H.; Liu, Z. J.; Khang, D. Y.; Huang, Y.; Rogers, J. A.; Lu, C.; Koh, C. G. Buckling of a stiff thin film on a compliant substrate in large deformation. Int. J. Solids Struct. 2008, 45 (10), 3107−3121. (14) Yin, J.; Yague, J. L.; Eggenspieler, D.; Gleason, K. K.; Boyce, M. C. Deterministic Order in Surface Micro-Topologies through Sequential Wrinkling. Adv. Mater. 2012, 24 (40), 5441−5446. (15) Lee, W.-K.; Kang, J.; Chen, K.-S.; Engel, C. J.; Jung, W.-B.; Rhee, D.; Hersam, M. C.; Odom, T. W. Multiscale, Hierarchical Patterning of Graphene by Conformal Wrinkling. Nano Lett. 2016, 16 (11), 7121−7127. (16) Cheng, H. Y.; Song, J. Z. A Simply Analytic Study of Buckled Thin Films on Compliant Substrates. J. Appl. Mech., Trans. ASME 2014, 81 (2), 024501. (17) Lee, W. K.; Engel, C. J.; Huntington, M. D.; Hu, J. T.; Odom, T. W. Controlled Three-Dimensional Hierarchical Structuring by Memory-Based, Sequential Wrinkling. Nano Lett. 2015, 15 (8), 5624−5629. (18) Lee, W. K.; Jung, W. B.; Nagel, S. R.; Odom, T. W. Stretchable Superhydrophobicity from Monolithic, Three-Dimensional Hierarchical Wrinkles. Nano Lett. 2016, 16 (6), 3774−3779. (19) Efimenko, K.; Rackaitis, M.; Manias, E.; Vaziri, A.; Mahadevan, L.; Genzer, J. Nested self-similar wrinkling patterns in skins. Nat. Mater. 2005, 4 (4), 293−297. (20) Efimenko, K.; Finlay, J.; Callow, M. E.; Callow, J. A.; Genzer, J. Development and Testing of Hierarchically Wrinkled Coatings for Marine Antifouling. ACS Appl. Mater. Interfaces 2009, 1 (5), 1031− 1040. (21) Huang, R. Kinetic wrinkling of an elastic film on a viscoelastic substrate. J. Mech. Phys. Solids 2005, 53 (1), 63−89.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b03498. Detailed analysis for G1 wrinkling; detailed analysis for G2 wrinkling (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Teri W. Odom: 0000-0002-8490-292X Present Address ∇

Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United States.

Author Contributions °

These authors contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Office of Naval Research (N00014-17-1-2482), the National Science Foundation (CMMI-1462633, CMMI-1635443), and the International Institute of Nanotechnology (IIN) at Northwestern University. This work made use of the Northwestern University Micro/ Nano Fabrication Facility (NUFAB), which is supported by the State of Illinois, Northwestern University, and Northwestern University’s Atomic and Nanoscale Characterization Experimental Center (NUANCE) facilities, which are supported by NSF-MRSEC and the MRSEC (DMR1121262). Y.X. and W.-K.L. gratefully acknowledge support from the Ryan Fellowship and the IIN.

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REFERENCES

(1) Chan, E. P.; Smith, E. J.; Hayward, R. C.; Crosby, A. J. Surface wrinkles for smart adhesion. Adv. Mater. 2008, 20 (4), 711−716. (2) Herminghaus, S. Roughness-induced non-wetting. Europhys. Lett. 2000, 52 (2), 165−170. (3) Lee, W.-K.; Jung, W.-B.; Rhee, D.; Hu, J.; Lee, Y.-A. L.; Jacobson, C.; Jung, H.-T.; Odom, T. W. Monolithic Polymer Nanoridges with Programmable Wetting Transitions. Adv. Mater. 2018, 30 (32), 1706657. (4) Dean, B.; Bhushan, B. Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Philos. Trans. R. Soc., A 2010, 368 (1929), 4775−4806. (5) Geim, A. K.; Dubonos, S. V.; Grigorieva, I. V.; Novoselov, K. S.; Zhukov, A. A.; Shapoval, S. Y. Microfabricated adhesive mimicking gecko foot-hair. Nat. Mater. 2003, 2 (7), 461−463. (6) Lee, W. K.; Yu, S. C.; Engel, C. J.; Reese, T.; Rhee, D.; Chen, W.; Odom, T. W. Concurrent design of quasi-random photonic nanostructures. Proc. Natl. Acad. Sci. U. S. A. 2017, 114 (33), 8734−8739. (7) Bae, W. G.; Kim, H. N.; Kim, D.; Park, S. H.; Jeong, H. E.; Suh, K. Y. 25th Anniversary Article: Scalable Multiscale Patterned Structures Inspired by Nature: the Role of Hierarchy. Adv. Mater. 2014, 26 (5), 675−699. (8) Huang, Z. Y.; Hong, W.; Suo, Z. Nonlinear analyses of wrinkles in a film bonded to a compliant substrate. J. Mech. Phys. Solids 2005, 53 (9), 2101−2118. E

DOI: 10.1021/acs.langmuir.8b03498 Langmuir XXXX, XXX, XXX−XXX