Supplementary information for Structural color printing via polymer-assisted photochemical deposition

Structural color printings have broad applications due to their advantages of long-term sustainability, eco-friendly manufacturing, and ultra-high resolution. However, most of them require costly and time-consuming fabrication processes from nanolithography to vacuum deposition and etching. Here, we demonstrate a new color printing technology based on polymer-assisted photochemical metal deposition (PPD), a room temperature, ambient, and additive manufacturing process without requiring heating, vacuum deposition or etching. The PPD-printed silver films comprise densely aggregated silver nanoparticles filled with a small amount (estimated <20% volume) of polymers, producing a smooth surface (roughness 2.5 nm) even better than vacuum-deposited silver films (roughness 2.8 nm) at ~4 nm thickness. Further, the printed composite films have a much larger effective refractive index n (~1.90) and a smaller extinction coefficient k (~0.92) than PVD ones in the visible wavelength range (400 to 800 nm), therefore modulating the surface reflection and the phase accumulation. The capability of PPD in printing both ultra-thin (~5 nm) composite films and highly reflective thicker film greatly benefit the design and construction of multilayered Fabry–Perot (FP) cavity structures to exhibit vivid and saturated colors. We demonstrated programmed printing of complex pictures of different color schemes at a high spatial resolution of ~6.5 μm by three-dimensionally modulating the top composite film geometries and dielectric spacer thicknesses (75 to 200 nm). Finally, PPD-based color picture printing is demonstrated on a wide range of substrates, including glass, PDMS, and plastic, proving its broad potential in future applications from security labeling to color displays.


Color retention time tests
The color retention time was also investigated by following experiments. Briefly, a 'Cactus' was printed on two dielectric-coated silver substrates with exactly the same film thicknesses (150 nm sputter-deposited SiO2 on 85 nm evaporated Ag), then 50 nm PMMA was spin coated on the one of them as an encapsulation layer. The microscopic images and reflectance spectra were taken immediately after color printing and after 14 days, respectively. The samples were stored in ambient condition during the whole experiments. The sample without an encapsulation layer showed a slight faded color after 14 days (Fig. S5a). From the reflectance spectra, the smaller modulation depth in the visible wavelength was found after 14 days due to oxidation of printed silver, which corresponded to less vivid color (Fig. S5c). On the other hand, the sample with an encapsulation layer still exhibited vivid color after 14 days in ambient condition (Fig. S5b).
Although the reflectance spectra indicated a slight red-shift, probably due to the additional reaction 5 between AgNPs and PMMA 1 , the modulation depth was observed to be similar as the pristine color, which implied that the color was well preserved by an encapsulation layer. Interestingly, the spin coated PMMA layer not only acted as encapsulation layer, but also increased color saturation behavior. Further investigation for the impact of various encapsulation layers on the color saturation and retention time will be studied.

Effective medium theory
In the classical model of free electron metals, the damping ( ) is determined by the scattering of the electrons with phonons, lattice defects, or impurities 2 . However, when particle size is comparable or smaller than the mean free path of the conduction electrons in the bulk material, scattering of the conduction electrons from the particle surface results in reduced effective mean free path ( ) and increased through the relation: where is the electron relaxation rate in the bulk material, is the Fermi velocity and A is a dimensionless fitting parameter related to scattering 3 . Take account of this phenomenon, the equation to calculate the permittivity of finite-sized metal nanoparticles ( ) must be modified as

2)
Here, is the frequency of incident light, is the permittivity for a bulk material, and is the plasma frequency 4 . In our case, we assume that AgNPs have spherical shape, hence the modified effective mean free path ( = 0.82 , where R is the radius of nanoparticle) is used for the calculation 5 . Fig. S9 shows of spherical AgNPs with various radius. In the visible wavelength range, the particle size effects are more strongly manifested in the imaginary part, while the real part indicates a very minimal differences. Since our PPD film acts as the absorbing material in the FP cavity, it is important to have better understanding of the correlation between particle size and permittivity which is closely related to the absorbance of materials. Figure S9. Size-dependent complex permittivities of spherical AgNPs as a function of wavelength.
Left: Real part. Right: Imaginary part.
Effective medium theory (EMT) has been widely used to characterize optical properties of inhomogeneous materials, e.g. metal/polymer nanocomposites 6 . Maxwell-Garnett introduced a separated-grain structure whose inclusion material is dispersed in a continuous host material, while Bruggeman suggested an aggregate structure which is filled with random mixture of the two constituents 7 . Since the reduction and polymer-assisted aggregation of AgNPs occur simultaneously in PPD process, we employ Bruggeman`s model to calculate the effective permittivity ( ) of PPD film. The formula for reads: where = 1.91 8 is the permittivity of polymer (pAAm) and is the filling factor of AgNPs in the nanocomposite 9 . The shape of AgNPs is very irregular in the real case (Fig. 2b), thus a shape factor is introduced as a fitting parameter to generalize the equation. To investigate the average AgNP size, we performed pAAm concentration dependent PPD printing. From the SEM images with various pAAm concentration (Fig. S11), we observed particles from < 5 nm to 10 nm with distinguishable contrast, particularly in 30 mM of pAAm concentration, which probably attributed to higher pAAm capping efficiency for AgNPs (Fig. S11e). Therefore, the average size of AgNPs was set as 10 nm in diameter for the purpose of calculating using our model. The measured complex permittivity ( = + ) of PPD film is obtained from the extracted spectroscopic ellipsometry data (Fig. 2d)