Auxetic Photonic Patterns with Ultrasensitive Mechanochromism

Abstract Photonic crystals with mechanochromic properties are currently under intensive study to provide intuitive colorimetric detection of strains for various applications. However, the sensitivity of color change to strain is intrinsically limited, as the degree of deformation determines the wavelength shift. To overcome this limitation, auxetic photonic patterns that exhibit ultra‐sensitive mechanochromism are designed. These patterns have a regular arrangement of cuts that expand to accommodate the strain, while the skeletal framework undergoes torsional deformation. Elastic photonic crystals composed of a non‐close‐packed array of colloidal particles are embedded in the cut area of the auxetic patterns. As the cut area amplifies the strains, the elastic photonic crystals show significant color change even for small total strains. The degree of local‐strain amplification, or sensitivity of color change, is controllable by adjusting the width of cuts in the auxetic framework. In this work, a maximum sensitivity of up to 60 nm/% is achieved, which is 20 times higher than bulk films. It is believed that the auxetic photonic patterns with ultra‐sensitive mechanochromism will provide new opportunities for the pragmatic use of mechanochromic materials in various fields, including structural health monitoring.


S1. Sensitivity of mechanochromic materials in literature
The degree of lattice deformation directly influences the diffraction wavelength shift.In the case of compression, the peak shift can be calculated as the product of the initial peak wavelength and the strain, represented as /0 = ε.The maximum sensitivity for this is 0/100 nm/%.Hence, the sensitivity cannot surpass 6.5 nm/% when 0 = 650 nm.For tensile strain, the maximum strain along the thickness direction is realized in purely elastic materials with a Poisson ratio of 0.5.Under these conditions, /0 = 0.5εx, and the highest theoretical sensitivity is 0/200 nm/%.As such, the utmost sensitivity is 3.25 nm/% for 0 = 650 nm.In Table S1, we summarize the sensitivity of mechanochromic materials previously reported.

S2. Fabrication of auxetic framework
The auxetic framework is fabricated by molding.A master mold with a positive pattern is prepared by 3D printing as shown in Figure S1a.The master mold is replicated to have the same design with PDMS, as shown in Figure S1b.A mixture of urethane acrylate and isobornyl acrylate in a weight ratio of 3:1 containing 1 w/w% photoinitiator is poured on the PDMS mold and cured by UV irradiation.The polymerized framework is released from the mold, as shown in Figure S1c.

S3. Reflectance spectrum of strain-free elastic photonic crystals
The regular arrays of silica particles in polymerized PEGPEA makes a reflection peak in the spectrum through Bragg diffraction.For example, the arrays of silica particles with an average diameter of 228 nm at the volume fraction of 0.40 show a peak at the wavelength of 676 nm, as shown in Figure S2.

S4. Mechanochromism of bulk photonic film
The elastic photonic film shows strain-dependent reversible color change due to the structural deformation of colloidal arrays in the film.As the strain increases from 0, the film turns from red to orange at 10% strain, green at 30%, and cyan at 50%, as shown in Figure S3a.The reflectance peak also blueshifts along with the strain, as shown in Figure S3b.The peak position is almost linear to the strain up to almost 50% strain at which the average slope is 2.9 nm/%, as shown in Figure S3c.There is a linear relation in the range of strain from 0 to 50%, where an average slope is 2.9 nm/%.

S5. Influence of framework materials
When urethane acrylate is used as a framework material without isobornyl acrylate, the modulus is relatively low and the blueshift of the photonic crystal in the cut area is relatively limited, as shown in Figure S4a.The use of the mixture of urethane acrylate and isobornyl acrylate in a weight ratio of 3:1 increases the modulus of the framework and provides enhanced degree of blueshift, as shown in Figure S4b.It seems that large modulus contrast between the framework and elastic photonic crystals enables the higher degree of strain localization in the cut areas.

S6. Reflectance spectra from local regions in double-cross
There is a regional variation of the degree of blueshift within a single cut element of doublecrosses.To study the variation quantitatively, the reflectance spectra are acquired from five different locations, as indicated in Figure S5a.The spectra at five locations are measured for various strains of 0, 1, 2, 3, 4, and 5%, as shown in Figure S5b-g.The degree of blueshift increases along with the strain, where the central region (#1) shows greatest shift.

S7. Amplification of local strain in auxetic framework
The auxetic framework amplifies strain in the cut areas.To compare the mechanical response of the framework with auxetic pattern containing photonic crystal, the framework is monitored during the expansion and the local strains in the double-cross and horizontal line are measured from image analysis, as shown in Figure S6.There is no significant difference in the local strains between the photonic crystal-free framework and the photonic crystal-embedded pattern, as shown in Figure S6c.

S8. Consistency of short rectangular cuts in reflectance spectrum and color
To study the consistent color preservation of the short rectangular cuts, we measure the reflectance spectra and optical microscope (OM) images under various strains, as shown in

S9. Reflectance spectra from local regions in horizontal line
There is a regional variation of the degree of blueshift within a single cut element of horizontal line.To study the variation quantitatively, the reflectance spectra are acquired from three different locations, as indicated in Figure S7a.The spectra at three locations are measured for various strains of 0, 1, 2, 3, 4, and 5%, as shown in Figure S7b-g

S10. Reversibility of the auxetic photonic patterns
To investigate the fatigue durability of the auxetic photonic patterns, we conduct cycling tests, as shown in Figure S9.Throughout 310 cycles between the total strains of 0 and 3%, no discernible change in the response is observed.This demonstrates the robustness and high stability of the patterns under repeated deformation.Furthermore, we observe the color change and recovery are instantaneous, occurring without any noticeable delay.

S11. Extension of auxetic photonic pattern until failure
The auxetic photonic patterns exhibit remarkable stability, with no plastic deformation or failure observed up to a maximum strain of 12%.The failure occurs at the interfaces between photonic material and auxetic framework at 13%, which gets worse along with the strain, shown in Figure S10.This high stability is achieved by producing a thin film of photonic materials that envelops the entire auxetic pattern.However, when the total strain exceeds 5%, a nonlinear response occurs due to the inherent limitations of the photonic materials.

S14. High resolution auxetic patterns
We can prepare high resolution auxetic patterns through photolithography and soft lithography.
For example, the mold for the auxetic pattern composed of arrays of three-pointed stars is prepared to have a line width of 100 μm and a length of 280 μm by photolithography technique, with which the auxetic pattern with void cuts is replicated by soft lithography using modified PU, as shown in Figure S13a.By following the same protocol for the macropatterns, we can produce photonic auxetic patterns with high resolution, as shown in Figure S13b.

S15. Description for Supporting Movies
• Movie S1: Mechanochromism in auxetic photonic pattern with a cut width of 1.4 mm.
• Movie S2: Reversible color change of auxetic photonic pattern during stretching and relaxation.
• Movie S4: Color change in double-cross of auxetic photonic pattern.
• Movie S5: Color change in horizontal line of auxetic photonic pattern.
• Movie S6: Reversible mechanochromism in auxetic photonic pattern with a cut width of 0.7 mm.

Figure S1 .
Figure S1.(a-c) Sets of schematic and photograph of master mold prepared by 3D printing (a), PDMS mold replicated from the master mold (b), and auxetic framework molded from the PDMS mold (c).

Figure S2 .
Figure S2.Reflectance spectrum of elastic photonic crystals composed of non-close-packed arrays of silica particles in polymerized PEGPEA matrix.

Figure S3 .
Figure S3.(a) Series of photographs of bulk elastic photonic film showing the gradual blueshift of color from red at strain-free state to cyan at 50% strain.(b) Reflectance spectra of bulk film taken at various strains as denoted.(c) Peak position as a function of strain.There is a linear

Figure S4 .
Figure S4.(a,b) Series of photographs of auxetic photonic patterns of which framework is made of polyurethane (a) and poly(urethane-co-isobornyl) (b).

Figure S6 .
Figure S6.(a,b) Series of OM images showing the gradual deformation of double-cross (a) and horizontal line (b) in the auxetic framework along with strain.(c) Local strains at the centers of double-cross and horizontal line as a function of total strain for auxetic framework and photonic patterns.

Figure
Figure S7.Notably, no changes are observed in the reflectance spectrum and color of the short rectangular cuts.This characteristic makes them a valuable reference for quantifying color changes during strain analysis.

Figure S7 .
Figure S7.(a, b) Reflectance spectra (a) and OM images (b) of the short rectangular cut for various strains as denoted.
. The degree of blueshift increases along with the strain, where the central region (#a) shows greatest shift.

Figure S9 .
Figure S9.Reversible change of reflectance peak position during 310 cycles of extension to 3% and relaxation to 0%.

Figure S10 .
Figure S10.Series of photographs of an auxetic photonic pattern with a width of 1.4 mm at three different strains, as denoted.

Figure S12 .
Figure S12.Series of OM images of the auxetic photonic pattern for various strains, as denoted.

Figure S13 .
Figure S13.(a) Photograph and OM image of the auxetic pattern with void cuts produced by photolithography and soft lithography.

Table S1 .
Comparison of sensitivity