Abstract:
The range of stretch-tunability of sinusoidal wrinkled surfaces that are obtained by compression of supported thin films is limited by the emergence of a period-doubled mode at high compressive strains. This disclosure presents a method to suppress the emergence of the period-doubled mode at high strains. This is achieved by compressing pre-patterned supported thin films, wherein the pre-patterns are substantially similar to the natural pattern of the supported thin film system. As compared to flat thin film systems, pre-patterned thin film systems exhibit period doubling behavior at a higher compressive strain. The onset strain for emergence of period-doubling is tuned by altering the amplitude of the pre-patterns.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    This invention relates to the method for low-cost manufacture of a physical topographic pattern and more particularly to the manufacture of stretch-tunable micro and nano scale sinusoidal periodic wrinkle patterns that are generated upon compression of supported thin films. 
         [0002]    Stretch-tenability extends the functionality of micro and nano structures by enabling the design and fabrication of active and adaptive systems that can respond to a variety of stimuli such as touch, temperature, humidity, and mechanical strain. Such active micro/nano-enabled systems have the potential to significantly impact diverse fields with direct societal benefits such as energy, water, health, and environment among others. For example, stretch-tunable structures find applications in the field of stretchable electronics, tunable optics, micro-nano fluidics, and sensing. Wrinkling of thin films is a low-cost process for fabricating such stretch-tunable structures over large areas. 
         [0003]    Sinusoidal periodic wrinkled patterns are formed via compression of supported thin films as a result of buckling-based instabilities and the mechanism is similar to Euler buckling of beams under compressive loads. A schematic of this process is illustrated in  FIG. 1 . Essential elements of a system that demonstrates wrinkle formation are: (i) a film  10  that is thin relative to the base, (ii) mismatch in the elastic moduli of the film and the base  12  with the film being stiffer than the base, and (iii) loading conditions that generate in-plane compressive strain (c) in the film. In such bilayer systems, the state of pure compression becomes unstable beyond a critical strain and wrinkles  14  are formed via periodic bending of the film/base. The natural period of wrinkles (λ n ) is determined by the competing dependence of strain energy on period in the film versus in the base. For small strains, the natural period depends only on the thin film thickness and the ratio of Young&#39;s moduli of the film and the base. At large strains, the natural period can be tuned to some extent by the strain; in addition, the amplitude (A) is determined by amount of applied compressive strain. Thus, stretch-tunable micro/nano structures can be fabricated via wrinkling. 
         [0004]    As the amplitude and the period of the wrinkles depend on strain, it is necessary to increase the feasible range of strain when high stretch-tenability is desired. The feasible range of strain is limited by the phenomenon of period doubling that occurs at high strains ( FIG. 2 ). When the compressive strain exceeds the nominal onset strain (ε 2,0 ), an additional period-doubled mode  20  emerges so that the single period sinusoidal structure transitions into a two-period structure. Emergence of this complex structure at high strains is often undesirable in applications that rely on a single-period structure. Thus, there is a need to suppress the onset of period doubling during fabrication of wrinkled structures. 
         [0005]    In the past, the strain dependence of stiffness modulus has been used to control the onset of period doubling 1,2 . In that method, period doubling is suppressed by increasing the amount of pre-stretch in the system. Such a method is limited by material selection as it relies on 2 nd  order nonlinear effects that arise from the dependence of material properties on strain. To overcome this material based limitation, one requires a suppression technique that does not rely on the stiffness versus strain material behavior. Herein, such a suppression technique is disclosed; this technique is based on geometric modifications to the system that can be applied either separately or in combination with the pre-stretch based method. Specifically, suppression of period doubling is achieved by performing the wrinkling process on pre-patterned surfaces instead of flat surfaces ( FIG. 3 ). in this disclosed method, the second critical strain for onset of period doubling (ε 2,p ) is controlled by changing the amplitude (A p ) of the pre-patterns  30 . With this technique, the operating range of stretch-tunable wrinkle-based devices can be increased by a factor of at least 1.5 with a modest pre-pattern aspect ratio of 0.15 (i.e., 2A p /λ n =0.15). 
       SUMMARY OF THE INVENTION 
       [0006]    The method of suppressing period doubling during generation of wrinkled structures according to this invention comprises replacing flat bilayer systems with pre-patterned bilayers such that the pre-patterns have the same period as the equivalent flat bilayer. When such a pre-patterned bilayer is compressed, the pre-patterns persist even when the bilayer is compressed beyond the nominal onset strain for the equivalent flat bilayer (ε 2,0 ); i.e., no additional mode emerges even at high strains. With further compression, the pre-patterned bilayer transitions into the period-doubled mode at a strain ε 2,p  that is higher than ε 2,0 . The equivalent flat bilayer is the bilayer system that is identical to the pre-patterned system in all respects, such as material properties and film thickness, except for the absence of the geometric pre-pattern. The suppression of period doubling can be tuned by controlling the amplitude of the pre-patterns; specifically, the onset strain for period doubling can be increased up to a limit by increasing the amplitude of the pre-patterns. 
         [0007]    The method of pre-patterning bilayers during fabrication of wrinkles is not novel. However, all previous demonstrations of pre-patterning have been used exclusively to increase the complexity of the wrinkles by generating hierarchical structures; i.e., to introduce an additional mode that is distinct from the pre-patterned mode. In contrast, this invention applies the pre-patterning technique to achieve the exact opposite effect, i.e., to prevent the emergence of an additional mode. This is achieved by ensuring that the pre-pattern period matches the natural period of the equivalent flat bilayer. On doing so, the pre-pattern period persists even beyond the strain at which the equivalent flat bilayer transitions into a complex period-doubled mode. This is an unexpected result as the period doubling phenomenon is distinct from the phenomenon of hierarchical wrinkle formation. Thus, this invention provides one with an easy-to-implement technique to suppress period doubling via well-characterized pre-patterning fabrication process steps. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1  is a schematic illustration of sinusoidal wrinkle formation during uniaxial compression of a flat bilayer system. 
           [0009]      FIG. 2  is a schematic illustration of period doubling at strains during uniaxial. compression of a flat bilayer system. 
           [0010]      FIG. 3  is a schematic illustration of wrinkle formation and suppression of period doubling during compression of a non-flat pre-patterned bilayer system. 
           [0011]      FIG. 4  is a schematic representation of the pre-patterning process based on replication of wrinkled surfaces. 
           [0012]      FIG. 5  illustrates finite element simulation results that demonstrate the effect of pre-pattern amplitude on the onset strain for period doubling. The pre-pattern period is identical to the natural period in these simulations. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0013]    Fabrication of wrinkled micro and nano scale structures via compression of flat bilayers is a well-developed art. One embodiment for fabrication of wrinkles has been previously disclosed in U.S. patent application Ser. No. 14/590,448 (“Biaxial tensile stage for fabricating and tuning wrinkles”). The process steps are: (i) pre-stretching a compliant base, (ii) generating a thin film on top of the stretched base, and (iii) releasing the pre-stretch in the base. In addition, the technique of pre-patterning the bilayers by using the wrinkled surfaces as molds has been previously disclosed in U.S. patent application Ser. No. 14/669,925 (“Wrinkled surfaces with tunable hierarchy and methods for the preparation thereof”) and Ser. No. 14/922,146 (“Method to fabricate pre-patterned surfaces during manufacture of complex wrinkled structures”). The contents of these three applications (Ser. Nos. 14/590,448; 14/669,925; and 14/922,146) are incorporated herein by reference. 
         [0014]    In one embodiment of the presently disclosed invention, period doubling at high strains is suppressed by performing a series of two wrinkle-patterning operations with an intermediate imprinting pattern transfer process between the two steps. This scheme is illustrated in  FIG. 3 . In the first wrinkle-patterning step one starts with a flat non-patterned bilayer system, whereas in the second wrinkle-patterning step one starts with a pre-patterned non-flat bilayer surface. The wrinkle pattern  40  obtained after the first step is utilized as a mold to generate the pre-patterned bilayer via replication. 
         [0015]    To enable the fabrication of wrinkle patterns, one must solve these sub-problems: (i) fabrication of flat and pre-patterned bilayer systems with the desired material properties and geometry and (ii) compression of the top stiff film. 
         [0016]    Stretchable bilayers with large stiffness ratio can be fabricated by attaching or growing a thin stiff film  10  on top of a thick elastomeric base  12 . For example, exposing a polydimethylsiloxane (PDMS) film to air or oxygen plasma leads to the formation of a thin glassy layer on top of the exposed PDMS surface via oxidation. Alternatively, a metallic or polymeric thin film may be deposited on top of PDMS to obtain the desired bilayer. The top  120  layer thickness can be tuned by controlling the duration of plasma oxidation or the deposition process; whereas the stiffness ratio may be tuned by selecting the appropriate top/bottom materials. In the preferred embodiment, both plasma oxidation and metal/polymer film deposition techniques are used to generate a stiff thin film on top of an elastomeric PDMS layer. 
         [0017]    Compression of the top film can be achieved by either directly compressing the bilayer or by generating a residual compressive strain in the top layer. As direct compression requires sustained loading to maintain the wrinkles, residual compression is often the preferred scheme. During mechanical loading, residual compression is generated by first stretching the PDMS base and then attaching/growing the stiff film on top of this pre-stretched base layer. On releasing the pre-stretch in the PDMS, the top layer undergoes compression that leads to formation of wrinkles. In the preferred embodiment of the pre-patterned bilayer, the pre-stretch is selected to be higher than the nominal period doubling onset strain for the equivalent flat bilayer. 
         [0018]    The pre-patterned bilayers are fabricated by using the wrinkled surfaces as the molds/templates to generate the top surface of the PDMS casts  44 . The curing process for fabrication of the pre-patterned base is same as that for the first wrinkling step and presented in U.S. patent application Ser. Nos. 14/669,925 and 14/922,146. Imprinting is performed by “gently” placing the pre-patterned coupon on top of the exposed surface of the curing PDMS  42  by aligning it to the direction of subsequent stretch 4 . Additionally, delayed imprinting is performed, i.e., imprinting close to, but before, the gelation point instead of at the beginning of the curing process. This ensures that the uncured PDMS is sufficiently viscous to support the pre-pattern during the curing process. One must be careful not to cross the gelation point as the phase change at this point prevents pattern replication. 
         [0019]    To ensure that no additional modes are generated during the second wrinkling step with the pre-patterned bilayer, the following conditions must be met: (i) the period of the pre-pattern must be ‘substantially similar’ to the ‘natural period’ of the bilayer system and (ii) the pre-pattern must be aligned along the subsequent stretch direction. 
         [0020]    Natural period: The natural period (λ n ) is the period of the pattern that is observed for an un-patterned flat bilayer system that has the same material properties as the pre-patterned bilayer system and is compressed by the same strain. The natural period of a bilayer system can be experimentally determined by eliminating the pre-pattern imprinting step from the sequence of steps shown in  FIG. 4 . It may also be estimated by the following relationship that is available in literature 3 : λ n =chη 1/3 . Here, ‘h’ is the thickness of the thin film, ‘η’ is the ratio of Young&#39;s moduli of the film to the base, and ‘c’ is a proportionality constant that depends on the Poisson&#39;s ratio of the film and the base. 
         [0021]    Substantial similarity: A substantially similar pre-pattern is one which leads to no growth  155  of an additional mode (i.e., no mode other than the pre-patterned period) when compressed up to at least the nominal onset strain for period doubling of the equivalent flat bilayer (ε 2,0 ). Ideally, the pre-patterned period must be identical to the natural period. However, this condition is impossible to achieve in a practical system. When the pre-pattern period is dissimilar from the natural period, hierarchical wrinkles are expected to emerge beyond a transition strain (ε t ). Nevertheless, due to the phenomenon of mode lock-in, the pre-pattern persists up to the transition strain. When the pre-pattern period is ‘substantially similar’ to the natural period, the transition strain for hierarchy (ε t ) is higher than the period doubling onset strain (ε 2,p ). Thus, during compression of such a ‘substantially similar’ bilayer one does not observe any additional modes at high strains. This ‘substantial similarity’ range can be easily obtained by experimental verification. A conservative estimate for this range can also be made by comparing the transition strain for hierarchy 4  (ε t ) with the nominal doubling onset strain for the flat bilayer (ε 2,0 ) as: 
         [0000]      (1+2 m   3 −3 m   2 ) 2 −12 k (1+2 m   3 )&lt;0   Eq. (1)
 
         [0000]    Here, m=λ p /λ n  and λ p  is the period of the pre-pattern. The non-dimensional parameter ‘k’ is given by: 
         [0000]    
       
         
           
             
               
                 
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         [0000]    Here, A p  is the amplitude of the pre-patterns. Pre-patterns that satisfy inequality (1) are guaranteed to be ‘substantially similar’. 
         [0022]    The onset strain for period doubling (ε 2,p ) can be tuned by controlling the amplitude of the pre-pattern (A p ). Finite element simulations were performed to verify the effect of pre-patterning on the onset strain. As shown in  FIG. 5 , the onset strain increases with an increase in the amplitude of the pre-patterns. 
         [0023]    It is recognized that modifications and variations of the present invention will be apparent to those of ordinary skill in the art and it is intended that all such modifications and variations be included within the scope of the appended claims. 
         [0024]    In one variation, the pre-patterns may be fabricated by a process other than wrinkling. In such a scheme, the manufacturing advantages of using a single fabrication process are lost. However, such a scheme may be necessary when pre-patterns are desired outside the feasible range of pre-patterns that can be fabricated via wrinkling. For example, pre-patterns may be fabricated via an alternate process when large amplitudes are desired. 
         [0025]    In another variation, biaxial strains can be applied during the pre-stretch step and the stretch can be released in sequence along the two directions so that high-aspect ratio wrinkles are formed along the pre-patterned direction followed by buckling along the other direction. The subsequent biaxially wrinkled pattern can be stretch-tuned along the pre-patterned direction over a range that is larger than that of an equivalent flat bilayer system. 
         [0026]    In another variation, biaxial strains can be applied during the pre-stretch step and the stretch along the two directions can be simultaneously released (at equal or unequal rate) so that a complex wrinkled pattern is formed that comprises of high-aspect ratio mode along the pre-patterned direction. This complex pattern can be stretch-tuned along the pre-patterned direction over a range that is larger than that of an equivalent flat bilayer system. 
       REFERENCES 
       [0000]    
       
         
           
             1. Auguste, A., Jin, L., Suo, Z., &amp; Hayward, R. C. (2014). The role of substrate pre-stretch in post-wrinkling bifurcations.  Soft Matter,  10(34), 6520-6529. doi: 10.1039/C4SM01038H 
             2. Chen. Y.-C., &amp; Crosby, A. J. (2014). High Aspect Ratio Wrinkles via Substrate Prestretch. Advanced Materials 26(32), 5626-5631. doi: 10.1002/adma.201401444 
             3. Groenewold, J. (2001). Wrinkling of plates coupled with soft elastic media. Physica A: Statistical Mechanics and its Applications 298(1-2), 32-45. 
             4. Saha, S. K., &amp; Culpepper, M. L. (2014). Wrinkled Surfaces With Tunable Hierarchy and Methods for the Preparation Thereof. U.S. patent application Ser. No. 14/669,925.