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October 23, 2015

C 2015 American Chemical Society

Nanoscale Surface Creasing Inducedby Post-polymerization ModificationKarson Brooks, Mir Jalil Razavi, Xianqiao Wang, and Jason Locklin*

Department of Chemistry, College of Engineering, and the Center for Nanoscale Science and Engineering, University of Georgia, Athens, Georgia 30602, United States

In soft polymeric materials, stresses be-yond a critical strain can trigger deforma-tions within the film, causing instabilities,

which have been directly related to failuremechanisms in several materials rangingfrom rubber tires to insulating cables.1�15

For this reason, polymeric films that undergobuckling, wrinkling, or creasing have gener-ally been avoided.3 However, in recent years,many groups have observed that program-ming these instabilities into soft materialscan actually improve function in certainpolymeric thin film devices,16�19 where con-trolled adhesion,20 cell patterning,21 andthe fabrication of deformable capillaries formicrofluidics22 all have been demonstrated.Having reproducible control over morpho-logical features is, therefore, an attractivequality in designing materials for a widevariety of applications. In particular, creasingis an instability which results from a largecompressive strain in a soft, elastic material.Many studies have shown excellent controlof induced creasing through the use ofexternal stimuli such as light,23 solvent,24,25

electric fields,10,26 temperature,7,27 and sur-face confinement;28 however, each of thesemethods results in structures with micro-scale features. Nanoscale creases have been

reported; however, these systems are rareand require physical cross-linking as well asan external stimuli.29,30 Here, we present asystem for fabricating controllable, reprodu-cible nanoscale surface instabilities using acombination of polymer brushes and reac-tive microcontact printing.Poly(pentafluorophenyl acrylate) ((poly)-

PFPA) is an activated ester polymer back-bone that is highly reactive toward nucleo-philes like primary amines,31 making it aprime candidate for post-polymerizationmodification (PPM). Our group has usedthis polymer backbone in combination withsurface-initiated polymerization to decoratesurfaces with a diverse collection of chemi-cal functionalities that can be used in avariety of thin film applications.32 We haveobserved that performing PPM using apoly(dimethlysiloxane) (PDMS) stamp inkedwith amino-terminated polymers throughmicrocontact printing (μCP) onto a reactivepoly(PFPA) brush layer leads to structureswith distinct creases throughout the filmthat resemble the structures of the sulci ofthe brain.33 Herein we report a highly re-producible method for generating surfacecreasing in which the nanoscale sizes andshapes of the creases can be controlled by

* Address correspondence tojlocklin@uga.edu.

Received for review July 6, 2015and accepted October 22, 2015.

Published online10.1021/acsnano.5b04144

ABSTRACT Creasing in soft polymeric films is a result of substantial compressive

stresses that trigger instability beyond a critical strain and have been directly related

to failure mechanisms in different materials. However, it has been shown that

programming these instabilities into soft materials can lead to new applications, such

as particle sorting, deformable capillaries, and stimuli-responsive interfaces. In this

work, we present a method for fabricating reproducible nanoscale surface instabilities

using reactive microcontacting printing (μCP) on activated ester polymer brush layers

of poly(pentafluorophenyl acrylate). The sizes and structures of the nanoscale creases

can be modulated by varying the grafting density of the brush substrate and pressure

applied during μCP. Stress is generated in the film under confinement due to the

molecular weight increase of the side chains during post-polymerization modification,

which results in substantial in-plane growth in the film and leads to the observed nanoscale creases.

KEYWORDS: nanoscale creasing . post-polymerization modification . polymer brushes

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changing the grafting density of the reactive esterbrush layer and the amount of force applied to thePDMS stamp during printing. This dependence on theshape and size of the creases is also corroborated usingcomputational simulations, which provides the abilityto predict and design surface creasing of varied shapesand sizes.

RESULTS AND DISCUSSION

The poly(PFPA) brushes used in this study weresynthesized through a photoinitiated free-radicalpolymerization from an asymmetric azo-based silaneinitiator, which was attached to silicon/silicon dioxidesubstrates through self-assembled monolayer (SAM)formation.34 In order to ensure a uniform graftingdensity throughout the substrate, the polymerizationwas carried out inside an inert atmosphere gloveboxusing a custom-built photoreactor to exclude oxygen.

A hand-held UV lamp (350 nm, 4.15W/cm2) was placeddirectly above the photoreactor, and the polymeriza-tion was carried out for a discrete period of time togenerate lower grafting density (2 h, 0.363 chains/nm2)and higher grafting density (5 h, 2.58 chains/nm2)polymer brushes. The resulting PFPA brushes all havea smooth topography, with an average root meansquared (rms) roughness of 2.65 nm as measured byatomic force microscopy. The side chain chosen forPPM was a hydrophilic Jeffamine M-2070 (HuntsmanCorp.), which is a 31:10 copolymer of poly(ethyleneoxide) and poly(propylene oxide) with a molecularweight of 2000 g/mol, where the terminal hydroxylgroup has been converted to an amine. The post-polymerization aminolysis reaction between theamino end group of the Jeffamine and the reactiveester of the poly(PFPA) backbone has been shownfrom previous experiments to be an extremely fastand efficient reaction with a pseudo-first-order rateconstant of ∼0.3 s�1.35 For reactive μCP (Scheme 1), a40 mM solution of Jeffamine M-2070 in toluene alongwith 80 mM of triethylamine was placed on the stampand dried under a stream of nitrogen. The stamp wasthen placed onto a PFPA brush substrate and allowedto react for 90 s. Different pressures were applied to thestamp by placing a weight of known mass uniformlyon top of the PDMS.First, Table 1 and Figure 1A describes the typical

result of a post-polymerization modification reactionon a polymer brush substrate when carried out insolution. The increase in molecular weight of the sidechain (MW = 2000 g/mol) results in an increase in theoverall thickness of the film.35�38 If one assumes thatthe grafting density of the polymer chains before and

Scheme 1. Post-polymerization modification of poly-(pentafluorophenyl acrylate) brushes using reactive micro-contact printing with a PDMS stamp inked with JeffamineM-2070.

Figure 1. AFM topography images of PFPA films functionalized with Jeffamine M-2070: (A) from solution, (B) μCP with apressure of 18.3 Pa, and (C) μCP with a pressure of 1.15 kPa.

TABLE 1. Thickness, Modulus, and Static Contact Angle Data for the Lower Grafting Density Poly(PFPA) Brushes

(0.363 chains/nm2) Used for Reactive Microcontact Printing with Different Pressures

original PFPA brush thickness (nm) pressure (Pa) brush thickness after PPM (nm) average QNM modulus (MPa) static contact angle (deg)

61.3 n/a n/a 99.1 96.261.3 18.3 121.2 20.8 52.161.3 124.3 117.4 16.6 46.461.3 1150.9 155.9 15.8 43.261.3 PPM in solution 242.3 <700 kPa 32.0

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after functionalization remains constant, the relation-ship between film thickness and molar mass can beexpressed as

L2L1

¼ M2F1M1F2

where L is the polymer brush thickness in the dry state,F is the bulk density, and M is the molecular weight.The subscript denotes the original (1) and Jeffamine-functionalized (2) polymer brush. After PPM, the brushthickness increases from 61.3 nm (L1) to 242.3 nm (L2),with near-quantitative conversion, as evidenced fromthe decreases in the PFPA carbonyl (CdO) stretch at1785 cm�1 and the aromatic ring stretch of the pendantgroup at 1523 cm�1 alongwith theobservanceof severalpeaks attributed to the PEG side chain (1100 cm�1) in theATR-FTIR (Figure 2). The filmmorphology is smooth, witha rms roughness of 2.3 nm. However, Figure 1B,C showsthe typical nanoscale creasing pattern observed whenthe PPM is performedusingmicrocontact printing. Thesefeatures are reproducible and consistent over multipleexperiments (more than 5with each pressure), whereweobserved the same average crease size and shape witheach trial.When a pressure of 18.3 Pa is applied on top of the

brush using the PDMS stamp, the creases observed aresmall, with an averagewidth of 107( 10 nm.When theprinting pressure is increased to 1.15 kPa, the creasingsize increases to a value of 203( 24 nm. To ensure thecreasing is a result of the confined reaction of Jeffaminewith the poly(PFPA) brushes and not a result of tolueneinteracting/swelling the PDMS stamp, the stamp wasinked using only toluene and placed in contact witha poly(PFPA) brush substrate. The morphology of thebrush was smooth and resembled that of Figure 1A,

indicating that the crease formation is a result of thepost-polymerization modification with Jeffamine. ATR-FTIR spectra of the films indicated a lack of full conver-sion, where the PFPA CdO stretch and the aromaticstretch of the pendant group are still present (Figure 2).In order to obtain information about the modulus

and adhesion of the film, PeakForce quantitative nano-mechanical mapping (QNM) was performed on thesubstrates.39 PeakForce quantitative nanomechanicalmapping is a scanning probe microscopy techniquethat allows for nanoscale property mapping of a sub-strate in real time. This is accomplished by oscillatingthe cantilever at a frequency below resonance andcollecting a force curve at each surface contact. Inaddition to maintaining a constant peak force, me-chanical information, such as the modulus and adhe-sion, can be extrapolated from these force curvesat each pixel, resulting in a map of the mechanical pro-perties like modulus and adhesion. Table 1 showsthe average QNM modulus, which was obtained byaveraging over the entire modulus map. The averagemodulus decreases steadily from 99.1 MPa for thepoly(PFPA) brush to 15.1 MPa for the brushes functio-nalized with increasing pressure. As a comparison, thePPM in solution has a modulus lower than 0.7 MPa,which is the lower limit of measurement for the tec-hnique. Using cone and plate rheometry (amplitudesweep at constant angular frequency of 10 rad/s), weobtained a storage modulus of 818 Pa for a Jeffamine-functionalized PFPA in solution, which matches wellwith the bottlebrush structure. The decrease in mod-ulus with increasing μCP pressure, therefore, indicatesa greater amount of Jeffamine in the brush after PPM,which is indicative of a higher conversion (aminolysis)deeper into the brush layer. It is important to note thatthe mechanical information obtained from PeakForceQNM is not absolute but rather qualitative in thecomparison of different mechanical properties be-tween substrates. While the modulus measurementsmay change slightly with differences in calibrationof the instrument and experimental setup, PeakForceQNM can serve as a useful tool for comparing a widearray of substrates if the experiments and calibrationsettings are performed consistently throughout experi-ments. PeakForce QNM aids in determining the me-chanism of crease formation particularly with respectto developing appropriate models for the simulationsas described below. The static contact angle of thesubstrates also follows a similar trend. Poly(PFPA) has astatic contact angle of 96.2�, due to the hydrophobicnature of the pentafluoroester backbone. A printingpressure of 18.3 Pa yields a contact angle of 52.1�, witha decrease to 46.4 and 43.2� for pressures of 124.3 Paand 1.15 kPa, respectively. As a comparison, the brushesfunctionalized with Jeffamine by PPM in solution arethe most hydrophilic, with an average value of 32.0�.The steady decrease in contact angle also provides

Figure 2. ATR-FTIR spectra of the low grafting density(0.363 chains/nm2) substrates. Upon μCP, the intensity ofthe ν(CdO) at 1785 cm�1 and the ν(C�F) at 1000 cm�1 fromthe carbonyl and fluorinated aromatic side chain begins todissipate,while the ν(C�O) at 1100 cm�1 from the JeffamineM-2070 ether increases. Solution functionalization results inthe full reaction of the poly(PFPA) brushes with JeffamineM-2070, but μCP under all conditions results in residualPPFA, indicating an incomplete reaction.

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evidence for higher conversion with increasing μCPpressure. The film thickness for each process does notfollow the same trend. While the PPM in solution yieldsa thickness increase of a factor of 4 (61.3 to 242.3 nm),the μCP with different pressures only increases thethickness by a factor of 2 for the 18.3 and 124.3 Pa anda factor of 2.5 for the 1.15 kPa samples.The creases observed in Figure 3 were reproduced

using computational simulations. In the models used,it was assumed that the effect of pressure due to theweight of the PDMS stamp correlated to the depth ofJeffamine penetration. With greater applied pressureand penetration depth, a larger extent of aminolysisand subsequent bottlebrush formation occurred. In themodels, the top layer of the plate was defined as thedepth of the film where Jeffamine had reacted withthe poly(PFPA) brush, and the bottom layer containedthe remaining unreacted poly(PFPA). Analytical andcomputational studies of a bilayer system have shownthat the wavelength of creases is proportional to thethickness of the top layer.38,40�42 As a result, a thinfilm on top of a soft material upon exposure to stressbeyond a critical value forms small-sized creases,whereas a thick film can form large-sized creases.In our experiments, as observed in the low graftingdensity (0.363 chains/nm2) cases, an increase inpressureleads to an increase in average crease size after post-polymerization modification. This trend suggests that alarger pressure results in more penetration of Jeffamineinto the brush layer during post-polymerization mod-ification, which results in the formation of a thickertop layer and creases with relatively large wavelengths.From Table 1, the thickness increases by a factor of2 upon creasing, which implies significant growthalong thedirectionnormal to thefilm. Figure 3Adisplaysa simulation with small creases, which were formedunder low-pressure conditions and correlate to theexperimental data shown in Figure 1B. Figure 3B haslarge-size creases simulated under a high pressure andcorrelate to Figure 1C. Here, the penetration depth ofthe Jeffamine into the film layer in the lower pressuresimulation is considered to be smaller than the high-pressure simulation. From the experimental results,we can assume that the ratio of the penetration depthin the twomodels is equal to 2,which is reasonable from

an analytical viewpoint since the wavelength of thebuckled thinfilmon the substrate is linearly proportionalto the thickness of the film.41 Due to the complex natureof the system, it is difficult to develop an exactmodel forthe surface functionalization. However, while simple indesign, the proposed bilayer model results in simula-tions that mimic the experimental results, giving insightinto the mechanism responsible for crease formation.When the μCP with different pressures is performed

on films of higher grafting density (2.58 chains/nm2),the distinct creasing morphologies change drastically(Figure 4A�C). Using a printing pressure of 18.3 Pa, thecreases have an average width of 417( 26 nm. Unlikethe lower grafting density films, increasing the printingpressure to 124.3 Pa results in a decrease in crease size(350( 36 nm). The size of the features decreases evenfurther when using a printing pressure of 1.15 kPa,where an average crease size of 243 ( 25 nm isobserved. The modulus and adhesion maps are alsoshown in Figure 4D�F and Figure 4G�I, along with theaverage modulus and static contact angle measure-ments provided in Table 2. Unlike the lower graftingdensity brushes, an increase in printing pressureresults in a steady increase in average modulus from14.0 to 21.0 MPa for a pressure increase from 18.3 Pato 1.15 kPa. The PPM in solution, however, still resultsin a modulus value less than 0.7 MPa. The increase inmodulus observed for the film's μCP with increasingprinting pressure is likely due to the extremely densepacking of polymer chains on the substrate, which aremore resistant to compression.43

The static contact angle decreases only slightlywith the increase in printing pressure, with an averagevalue ranging from 55 to 53�. Also, an increase infilm thickness for each substrate is observed with anincrease in printing pressure, from an original valueof 435.8 to 459.2, 515.1, and 736.6 nm for the 18.3 Pa,124.3 Pa, and 1.15 kPa, respectively. Like the lowergrafting density brushes described above, this valueis still significantly less than the increase in film thick-ness that occurs when PPM is performed in solution(435.8 to 1410.0 nm).For both the lower grafting density (0.363 chains/

nm2) and higher grafting density (2.58 chains/nm2)brushes, the macromolecular monolayers are cova-lently linked to the substrate during the polymeriza-tion, which leads to a constant grafting density for thepolymer layer before and after the PPM is performed.When the PDMS stamp inked with Jeffamine is placedinto contact with the PFPA brush layer, the reactivespecies can penetrate, solvate, and react with the PFPAbrush layer, which generates a large change in themolecular weight of the grafted polymer, leading to anincrease in film thickness. In μCP, the PDMS stampconfines or restricts growth normal to the surface, andtherefore, the stress resulting in the film from PPMcauses in-plane growth in the film, which leads to the

Figure 3. Morphological simulations of the low graftingdensity substrate after post-polymerization modificationusing μCP for (A) 18.3 Pa and (B) 1.15 kPa.

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observed nanoscale creases. This creasing due toin-plane growth is similar to the phenomenon thatoccurs when a cross-linked gel is swollen in responseto a favorable stimulus.1,9,24,27,30

In the lower grafting density films, the increasingsize of the creases with increasing pressure is likely dueto the increased penetration of the Jeffamine into thebrush layer. This trend is also evident in the decreasedmodulus and static contact angle values for the filmsfabricated with increased pressure. With respect to thehigher grafting density films, the crease size actuallydecreases with increasing pressure, likely due to lessfree volume available for in-plane deformation. This isalso evident in the increasing modulus of the films,which are more resistant to compression.It is important to note that the pressures applied

to the PDMS stamps during printing are notably low.

However, as evidenced by changes in thickness, con-tact angle,modulus, and adhesion, post-polymerizationmodification on each substrate does take place to yieldfilms with different properties and morphologies.This trend indicates that the small and subtle pres-sures applied are sufficient to alter penetration andsolvation of the brush undergoing PPM. We haveexhausted every other variable (to the best of ourability) besides the amount of pressure applied to thePDMS stamp, and this consistently results in creases ofdifferent sizes.Computational simulations for the high grafting

density substrates are shown in Figure 5. For thesesubstrates, although more penetration of Jeffamineinto the brush is expected with larger pressures on topof the film, the changes in thickness are not remark-able, which indicates that the acting pressure causes

TABLE 2. Thickness,Modulus, and Static Contact AngleData for HighGraftingDensity Poly(PFPA) Brushes (2.58 chains/nm2)

Used for Reactive Microcontact Printing with Different Pressures

original PFPA brush thickness (nm) pressure (Pa) brush thickness after PPM (nm) average QNM modulus (MPa) static contact angle (deg)

435.8 n/a n/a 107.0 94.3435.8 18.3 459.2 14.0 54.6435.8 124.3 515.1 16.8 53.3435.8 1150.9 736.5 21.0 53.0435.8 PPM in solution 1410.0 <700 kPa 33.4

Figure 4. AFM topographic (A�C), modulus (D�F), and adhesion (G�I) data for PFPA films functionalized with JeffamineM-2070 by μCP. (A,D,G) 18.3 Pa, (B,E,H) 124.3 Pa, and (C,F,I) 1.15 kPa.

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confinement in the direction perpendicular to the sub-strate, resulting in greater growth along the in-planedirection rather than the normal direction. In the FEmodels, the growth factor was adjusted to account forgreater in-plane growth rather than growth normal tothe surface. The growth ratio in each direction is basedon the crease size ratio obtained from the experimentalresults. Greater in-plane growth results in the top layerhaving a lower thickness, which ultimately leads tosmaller-sized creases. Although the total thicknesschange of the film is larger in the high-pressure casethan in the low-pressure case, the thickness of thetop layer due to post-polymerization modification isstill relatively small. This may explain the inverse trendin crease size observed in the high grafting densitysubstrates.In Figure 5A, which correlates to the experimental

morphology in Figure 4A under the lowest pressure,the growth normal to the surface is greater than that ofin-plane growth, resulting in the formation of a thickfilm with large creases. Contrary to the low-pressureexperiments, the influence of a greater pressure on thePDMS stamp leads to a change in the growth patternfrom the direction normal to that of in-plane. Thesesimulations are shown in Figure 5B,C and correlateto the experimental data in Figure 4B,C, respectively.This subtle change creates a film with smaller thick-ness changes, which produces smaller creases in thefilm. These simulations are in agreement with the

experimental results and can further be corroboratedin Figures S2 and S3, which display the crease sizeratios and amplitude ratios for the simulations andexperimental data.

CONCLUSION

Using μCP on poly(PFPA) brushes, we have intro-duced a method to both fabricate and control nano-scale creasing in ultrathin films using simple post-polymerization modification. The versatility of thismethod and ease of fabrication allows the generationof creases with controlled size simply by varying thepressure applied to the stamp during the printing pro-cess. This method was corroborated with simulations,which may allow for creased surfaces that can be easilymanipulated for a desired application. Also, the reactivepolymerused for PPMcanbevaried in termsofmolecularweight and chemical functionality, which should openthe door to awide variety of applications in areas such asnanoparticle-directed assembly, thin filmswith increasedsurface area, sensors, and stimuli-responsive coatings.Since the measurement of penetration depth andgrowth ratio in experiments is a challenging question,computational methods can help to further elucidatethis process as well as quantify the crease morphologies.We are further investigating the subtle effects of pressureon the reactive printing process, as well as the influenceof surface tension to further elucidate the mechanism ofcrease formation in these thin films.

MATERIALS AND METHODS

Materials. Siliconwafers (orientation Æ100æ, native oxide) werepurchased from University Wafer. The PDMS stamps were madeusing a SYLGARD 184 silicone elastomer kit from Dow Corning.Solvents were purified using an MBraun purification system(MB-SPS). Jeffamine M-2070 was provided as a gift by HuntsmanChemical. All other chemicals were purchased from Sigma-Aldrich or TCI and were used as received.

Polymer Brush Synthesis. PFPA was synthesized followingpreviously reported methods.31 It was further purified using aplug of neutral alumina with DCM as eluent to remove anyresidual acrylic acid. The AIBN-silane initiator was also preparedusing previously reported methods and, after synthesis, storedimmediately in an inert atmosphere glovebox.34 Silicon waferswere cut using a diamond scribe and cleaned by sonicationin hexanes, isopropyl alcohol, acetone, and deionized water for1min each. The slideswere then cleaned using argon plasma for

5 min (Harrick Plasma PDC-32G) and subsequently placed in aslide stainer and transferred to an inert atmosphere glovebox(MBraun Labstar). A 10 mM solution of the AIBN-silane initiatorwas prepared in 20 mL of dry toluene in a scintillation vial.The vial was shaken vigorously to ensure full dissolution of theinitiator and added to the slide stainer for 16 h. After 16 h, theinitiator solution was removed and replaced with fresh toluenefor storage until use. PFPA was degassed by bubbling argonthrough a needle at 0 �C and transferred to an inert atmosphereglovebox. An initiator substrate was sonicated in fresh tolueneto remove any physisorbed material. The substrate was thendried under a stream of nitrogen and transferred back into theglovebox. The substrate was placed on a microscope slide(Fisherbrand precleanedmicroscope slides), and 300 μL of PFPAwas added by pipet to the substrate. Another microscope slidewas sandwiched on top of the substrate and clamped with fourbinder clips to ensure intimate contact. A hand-held UV lamp

Figure 5. Morphological simulations of a high grafting density substrate for (A) 18.3 Pa, (B) 124.3 Pa, (C) 1.15 kPa.

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(350 nm, 4.15 W/cm2) was placed above the substrate, and thepolymerization was carried out for 2 h for the thinner substrates(lower grafting density, 0.363 chains/nm2) and 5 h for the thickersubstrates (higher grafting density, 2.58 chains/nm2). After thereaction was complete, the substrate was removed from the UVirradiation source. A glassy polymer formed on the substrate,which was removed and collected for gel permeation chroma-tography. To remove the remaining glassy polymer betweenthe wafer and the microscope slide, the substrate was Soxhletextracted in tetrahydrofuran (THF) overnight. Gel permeationchromatography (GPC) was conducted on a liquid chromato-graph (Shimadzu LC-20AD series) equipped with a RID-10Arefractive index detector. Polymer samples were diluted inTHF mobile phase and passed through three PhenomonexPhenogel (10E3A, 10E4A, and 10E5A) columns at 40 �C undera constant volumetric flow rate (1 mL min�1). Molecular weightcharacteristics of the samples were referenced to polystyrenestandards (Agilent Technologies EasiCal PS-2). The polymerfrom the thinner substrate had a Mn of 148 034 Da with a^ of 1.58. Themolecular weight of the polymer from the thinnersubstrates was used to estimate the grafting density forboth brushes since we were unable to isolate enough polymerfrom the longer polymerization time to get molecular weightinformation by GPC.

PDMS Stamp Fabrication. A 10:1 elastomer to curing agentmixture was made of the SYLGARD 184 silicone elastomer kit.The mixture was poured over a glass microscope slide in a Petridish and cured for 2 h at 70 �C. After 2 h, the patterned stampwas cut from the remaining PDMS and cleaned with acetone,ethanol, and Scotch tape.

Creased Film Formation. Two milliliters of a 40 mM solution ofJeffamine M-2070 was prepared in toluene with 80 mM oftriethylamine. The solution was inked onto the PDMS stampusing a cotton swab, and the solvent was evaporated under astream of nitrogen. This was repeated several times in order toensure a uniform coverage on the stamp. The stamp was thenplaced on the polymer brush substrate for 90 s. The substratewas then rinsed vigorously with toluene and dried under astream of nitrogen. In order to obtain different pressures, theweights of the stamp and the weight added to the top of thestamps were varied. In the case of additional weight, sand wasplaced in vial to equal the weight needed to obtain a certainpressure.

Substrate Characterization. The wrinkled morphologies of thesubstrates were collected using a PeakForce QNM (BrukerMultimode AFM, Scanasyst-AIR, k= 0.4 N/m, resonant frequency(f0) = 50�90 kHz). A 10 and 3 μm scan was taken for eachsubstrate. The average number of creases for each substratewas calculated by measuring the distance from the end of acrease to the middle of a neighboring crease using NanoscopeAnalysis Software (Bruker) and taking an average from over30 different line profiles. The infrared spectra of the substrateswere taken using a Nicolet model 6700 with a grazingangle attenuated total reflectance accessory at 256 scans witha 4 cm�1 resolution. The thicknesses of the thinner polymerbrushes were measured using a M-2000 spectroscopic ellips-ometer (J.A. Woollam Co., Inc.) with a white light source at threeangles of incidence (65, 70, and 75�) to the silicon wafer normal.The data were modeled using a Cauchy layer with an extinctioncoefficient of 0 and refractive index of 1.50 for the polymerbrush layer. The thicker polymer brushes were measured usinga Veeko Dektak 150 with a 3 mm radius stylus. Rheometry wasperformed using an Anton Paar modular compact rheometer(MCR 302), using an amplitude sweep at a constant angularfrequency of 10 rad/s.

Computational Methods. To find the deformation field of agrowing film in a bilayer model, decomposition of deformationgradient theory was carried out. Deformation gradient, F, isrepresented through the elastic tensor, A, which induces stressand a growth tensor, G, which causes volume change.

F ¼ A 3G

Here, F = ∂x/∂X andmaps the initial configuration to the currentconfiguration. Although both G and A tensors may be in-compatible deformations, their multiplication, F, should be a

compatible deformation.44 Generally, the basic concept is validto both isotropic and anisotropic growth. Among other factors,the growth tensor typically depends on the stress state anddeformation. For simplicity, it was assumed that the growthprocess has a known spatial distribution, insinuating that allof the information is independent of stress.45 The boundaryvalue problem of the swollen gel is also equivalent to thatof a hyperelastic solid.46 The growth of soft film can, therefore,be modeled by a hyperelastic material with a strain energyfunctionW(A), where the Cauchy stress, σ, is related to the strainenergy function by

σ ¼ ADWDA

� pI

where p is the hydrostatic pressure and I is a second-order unitvector.45 In the absence of any body force, the mechanicalequilibrium imposes

div σ ¼ 0

where “div” is the divergence operator in the current con-figuration. There are several proposed material behaviors forhyperelastic materials. Here, the Fung model was implementedand is given by

W ¼ c

2(eQ � 1)

where c is a constant and Q is a function of the three principalstrain components.

To predict the morphologies after the onset of instability inthe growing polymer brush, a computational model based onnonlinear finite element with anisotropic growth in a bilayerfilm was carried out. In the computational model, a soft platewhich mimics the polymer brush film is partitioned to the twolayers; the top layer mimics the growing soft film with chemicalreactions due to the polymerization process, and the bottomlayer is considered as the relatively stiff substrate, as shown inFigure S1. Determination of the thickness in the bilayer modelwas based on experimental results and analytical predictions.The thickness ratio of the bilayers in the different models wasdetermined based on the size of creases from the experimentalresults. For the growth ratio in the normal and in-plane direc-tions, we considered different mechanisms for the low and highgrafting density cases. The bottom surface of the substrate layerwas fixed, and symmetry boundary conditions were employedalong the sides of the soft plate. To maintain the accuracy andefficiency of the computational model, a soft plate with mod-erate dimensional sizes was chosen to produce the creasingpatterns. Growth of the film is considered as the anisotropicgrowth, which allows growth to be controlled in normal and in-plane directions. The growth was simulated via thermal expan-sion; anisotropic growth was modeled by adjusting differentthermal expansion coefficients in different directions.47,48 Theouter surface of the filmmodelwas allowed tobe in self-contact,and small structuredmesh is distributed in themodel. Dynamic-Explicit solver, which is suitable for large deformations and bothnonlinear and quasi-static problems, was implemented to per-form the morphological changes in the growing film. In thedynamic model, the inertial force acts as the perturbation totrigger instability. Deformation patterns after instability are notguaranteed to be exactly symmetric, even though the initialmodel is symmetric.49 Robustness studies concluded that as longas themesh size is small enough, then the qualitative features ofthe model do not depend onmesh size. The creased patterns ofthe model after growth and instability do not depend on theabsolute values of the elastic moduli for the film and substrate;they only depend on the modulus ratios. Material properties ofthe film are considered to be growth-dependent since theseproperties show a decreasing trend as the reaction time goes onbased on the experimental data (Figure S4).50

Conflict of Interest: The authors declare no competingfinancial interest.

Supporting Information Available: The Supporting Informa-tion is available free of charge on the ACS Publications websiteat DOI: 10.1021/acsnano.5b04144.

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Additional information on the methods used for the simula-tions (PDF)

Acknowledgment. We acknowledge the National ScienceFoundation (DMR 0953112 and NSF GRFP 1011RH252141) forfunding this work.

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