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1 advances.scienceag.org/cgi/conen/full/3/9/e /dc1 Suppleenary Maerials for Bioinspired brigh noniridescen phoonic elanin supraballs Ming Xiao, Ziying Hu, Zhao Wang, Yiwen Li, Aleandro Diaz Toro, Nicolas Le Thoas, Boxiang Wang, Nahan C. Gianneschi, Mahew D. Shawkey, Ali Dhinowala The PDF file includes: Published 15 Sepeber 2017, Sci. Adv. 3, e (2017 DOI: /sciadv Opical Model able S1. Condiions used for synhesizing differen sizes of CS-SMNPs. fig. S1. UV-vis absorpion specra of pure SMNPs, CS-SMNPs, and pure silica nanoparicles in aqueous soluion (20 g/lier. fig. S2. Represenaive TEM iage of a sall supraball ade of 160/0-n CS- SMNPs. fig. S3. FDTD siulaions of reflecance specra a noral incidence using he diensions of he core-shell paricles in supraballs. fig. S4. Coparisons of reflecance specra colleced for single supraballs ade of elanin, core-shell nanoparicles, and ixures of elanin and core-shell nanoparicles. fig. S5. TEM iages of he inner srucure of supraballs of binary CS-SMNPs. fig. S6. Noral reflecance specra of supraballs ade fro 160/66- and 160/36- n CS-SMNPs, and supraballs ade by ixing differen raios of 160/66- and 160/36-n CS-SMNPs. fig. S7. Calculaions of inverse of noralized ranspor ean free pah as a funcion of differen ixing raios of 160/36- and 160/66-n CS-SMNPs using he scaering heory oulined in SI. fig. S8. Iage of a drop of waer on an OTS-coaed glass. References (33 44 Oher Suppleenary Maerial for his anuscrip includes he following: (available a advances.scienceag.org/cgi/conen/full/3/9/e /dc1

2 ovie S1 (.p4 fora. Supraball-pained flowers do no change colors when he saple is roaing a differen angles.

3 Opical Model FDTD siulaion We used Luerical FDTD soluions 8.15 o run he opical odeling. In he siulaion, we creaed an FCC colloidal laice wih is plane (111 as X-Y plane and a plane wave ligh was ineced down fro Z direcion, perpendicular o plane (111. For he siulaion in Fig. 1B, we copared heoreical reflecance specra fro core-shell and hoogenous nanoparicles. The hoogenous nanoparicles is he sae size as core-shell nanoparicles wih a RI of averaged RI value of core-shell nanoparicles based on he equaion n ( hoo V + V = n V + n V core shell core core shell shell (1 We se he RI value of 1.74 for high RI aerial (idenical o synheic elanin, bu wihou any absorpion and 1.45 for he low RI aerial (sae wih fused silica in our calculaions. The laice has 30 periods along he X and Y direcions and 12 periods along Z direcions. We chose auo non-unifor esh ype wih accuracy of 6 and a ligh source range of n (esh size is around 8 n. Boh core and shell aerials conained no absorpion so ha we could decouple opical response fro he core-shell srucures and absorpion. When coparing siulaion resuls wih experienal reflecance of supraballs (Fig. 3D, we considered absorpion fro SMNPs core (19. In his calculaion, he Luerical sofware used RI values fro fiing of boh he real par and iaginary par of RI values based on experienal daa (fig. S3A. Based on our observaion

4 ha only he op 5~10 layers of supraball conribues o he colors, we calculaed only 6 layers along z direcions. We chose auo non-unifor esh ype wih accuracy of 5 and a ligh source of n (esh size is around 5 n. Scaering heory Because he supraballs ade of ixed ype 1 (160/36 n and ype 2 (160/66 n CS-SMNPs are far fro he ordered FCC packing (Fig. 5C, we can no siply regard he as phoonic crysals. To consider he disorder effec, we used he uliple scaering heory o explain he color shifing fro blending wo sizes of CS-SMNPs wih differen ass raio (27, 28. The uliple scaering heory of ligh can provide basic analyical ehods o address ligh scaering proble in disordered phoonic edia. To predic he reflecance specra profile analyically wihou resoring o ie-consuing nuerical siulaions, here we define he paraeer A ( k l 1 = o presen he diffuse reflecance of he supraballs, where k0l = 2 πl / λ Firs, l direcly deerines he diffuse reflecance of supraballs, which plays a key role in he producion of srucural colors. For 0 he diffusive ligh ranspor wihou absorpion, ransission is proporional o l as T ~ l and hus reflecance increases when l is reduced (27, 28. When he opical absorpion of CS-SMNPs is considered, he reflecance is sill negaively relaed o l, because saller l leads o a sronger uliple scaering effec (noe l doesn rely on absorpion, which is he only source of backscaering and hus diffuse reflecance (27, 28. Secondly, here are significan inerference effecs when l is coparable wih he wavelengh λ ( A ~ 1, which are also observed in he scenarios such as coheren backscaering (33 and Anderson localizaion (34.

5 Consrucive inerference effecs lead o a reducion in diffusion consan D (i.e. coheren 2 backscaering gives rise o a correcion as D / D ~ A (35 and hus an increase in reflecance, which can be also quanified by he paraeer A. Therefore, we can use he paraeer A o esiae specral profile of diffuse reflecance. This paraeer has also been used by F. Scheffold e al in predicing opical specra of densely packed TiO 2 nanoparicles (36. Since CS-SMNPs are densely packed in supraballs, he shor-range order induced inerference echanis aong binary CS-SMNPs in uliple scaering of ligh likely plays a key role in l as well as he observed reflecance specra ( To suppor his arguen, here we consider he shor-range order induced inerference effec in he uliple scaering using a heoreical odel where wo-paricle correlaion is aken ino accoun (known as Born s approxiaion (39. Then we copare his resul wih ha fro he independen scaering approxiaion (ISA wihou consideraion of he shor-range order (27, 28, 35. The heoreical odel predics he ranspor ean free pah of ligh in supraballs as l ( ρσ 1 σ is calculaed in he following expression (39 = where ρ is he nuber densiy of paricles. π π σ = B( θ sin θ (1 cos θ dθ 2 k 0 (2 where k = 2 πn eff / λ and B( θ = αf11 ( θ S11( θ + (1 α F22 ( θ S22( θ + 2 α(1 α F12 ( θ S12 ( θ. We calculae effecive refracive index n eff = ε using he Maxwell-Garne forula for eff hree-coponen ediu (core, shell, and air as (40

6 ε eff 1 core 1 shell 1 f ε core f ε = + shell ε + 2 ε + 2 ε + 2 (3 eff core shell where r r f = f + f and core 3 3 1,core 2,core r1,oal r2,oal 3 3 r 1,core r 2,core fshell = f1 1 + f r 1,oal r 2,oal. f and 1 f 2 are he volue fracion of ype 1 and ype 2 CS-SMNPs. ε core and ε shell are periiviy of core (synheic elanin and shell (silica. r and 1,core r are he core radius and oal radius of ype 1 1,oal CS-SMNPs, while r and 2,core r are he core radius and oal radius of ype 2 CS-SMNPs. 2,oal α = N / ( N + N is he nuber fracion of ype-1 CS-SMNPs. S ( θ, S ( θ, and S ( θ are parial srucure facors of he binary-paricle syse calculaed based on Percus-Yevick hard sphere odel (41. The Percus-Yevick odel is a sufficien approxiaion for calculaing pair correlaion funcion characerizing shor-range order in packing hard-sphere syses. F ( θ, 11 F ( θ, and 12 F ( 22 θ are for facors derived fro he Mie heory for core-shell paricles. They are calculaed as follows F ( θ = fs fs + f p f p * * (4 F ( θ = fs fs + f p f p * * (5 * * F12 ( θ = Re fs1 fs2 + f p1 f p2 (6

7 where fs ( θ = (2 + 1 a, τ(cos θ + b, π(cos θ and fp ( θ = (2 + 1 a, π(cos θ + b, τ(cos θ wih = 1 = 1,2 denoing differen paricle species. Here τ and π are funcions defined as = 1 P 1 (cos θ π(cos θ = and sinθ dp 1 (cos θ τ (cos θ =, where dθ P 1 (cos θ is he associaed Legendre funcion. a, and b, are Mie coefficiens calculaed as (42, 43 a, = ( ɶ ( D, / nshell + / y ψ ( y ψ 1( y Dɶ / n + / y ξ ( y ξ ( y (7, shell 1 b, = ( ɶ ( nshellg, + / y ψ ( y ψ 1( y n Gɶ + / y ξ ( y ξ ( y (8 shell, 1 where y = kr is he size paraeer for he oal radius of ype- paricle and k = 2 πn eff / λ is,oal he wavenuber in he surrounding ediu wih effecive refracive index n eff as calculaed previously. We defined n = nshell / ncore, where n shell = ε shell and ncore = ε core are coplex refracive indices of shell and core aerials. The paraeers, D ɶ,, G ɶ, are calculaed as Dɶ, = D ( n y A χ ( n y / ψ ( n y shell, shell shell 1 A χ ( n y / ψ ( n y, shell shell (9 Gɶ, = D ( n y B χ ( n y / ψ ( n y shell, shell shell 1 B χ ( n y / ψ ( n y, shell shell (10

8 And, A, B, are nd ( ncore x D ( nshell x A, = ψ ( nshell x nd ( n x χ ( n x χ ( n x (11 core shell shell D ( ncore x / n D ( nshell x B, = ψ ( nshell x D ( n x χ ( n x χ ( n x (12 core shell shell where x = kr is he size paraeer for he core radius of ype- paricle. In above equaions,,core ψ ( α, ξ( α and D ( α are special funcions defined using arguen α as ψ ( α = α ( α, χ ( α = α y ( α, ξ α = α α and D ( α = ψ ( α / ψ ( α. Here ( α, y ( α and (1 ( h ( h (1 ( α are spherical Bessel funcions of he firs kind and second kind, and spherical Hankel funcion of he firs kind, in he order of n respecively (42. ψ ( α and χ ( α denoe he firs-order derivaive respec o arguen α. Equaions (7-12 are also applicable for hoogeneous spheres by seing r,oal = r,core. We calculaed he A paraeer for supraballs consising of binary CS-SMNPs wih differen ass raios. fig. S7A showed he noralized A for differen ass raios for 160/36 n and 160/66 n CS-SMNPs. A clear rend of blue-shif was observed when increasing he aoun of 160/36 n CS-SMNPs, which is consisen wih he experienal observaion. As a coparison, we also calculaed A wihou consideraion of shor-range order and inerference effecs (fig. S7B, where we se he parial srucure facors S11( θ = S22( θ = 1,

9 S ( θ = 0 and wavenuber 12 k = k0 = 2 π / λ, unlike using k = 2 πn eff / λ in he shor-range-order case because using he effecive index also akes parial inerference effecs ino accoun (44. This approxiaion for calculaing ranspor ean free pah is called independen scaering approxiaion (ISA (44. No significan shif of peaks was observed by changing he coposiion of binary CS-SMNPs, which was invalid according o experienal resuls. This finding suppors our conclusion ha shor-range order plays he crucial role in producing he blended colors of supraballs when ixing binary sizes of CS-SMNPs.

10 Supporing Table and Figures able S1. Condiions used for synhesizing differen sizes of CS-SMNPs. Supraball Colors Core diaeer (n Shell hickness (n TEOS (μl Reacion Tie Red 160 ± 7 66 ± h Orange 160 ± 7 50 ± h Olive 160 ± 7 36 ± in Blue-green 123 ± ± h Navy 123 ± ± in fig. S1. UV-vis absorpion specra of pure SMNPs, CS-SMNPs, and pure silica nanoparicles in aqueous soluion (20 g/lier.

11 fig. S2. Represenaive TEM iage of a sall supraball ade of 160/0-n CS-SMNPs. fig. S3. FDTD siulaions of reflecance specra a noral incidence using he diensions of he core-shell paricles in supraballs. (A The real and iaginary refracive indices for synheic elanin paricles used in he FDTD calculaions (hese values were calculaed based on our previous published resuls (19. (B Coparisons of heoreical noral reflecance specra (FDTD for supraballs coposed of hree differen sizes of CS-SMNPs wih (solid lines and wihou (dash lines considering absorpion of elanin.

12 fig. S4. Coparisons of reflecance specra colleced for single supraballs ade of elanin, core-shell nanoparicles, and ixures of elanin and core-shell nanoparicles. (A Reflecance of single supraballs ade of pure 160/0-n, ixed 160/0-n & 160/36-n CS-SMNPs, and ixed 160/0-n & 160/66-n CS-SMNPs. (B Reflecance of single supraballs ade of pure 160/36-n CS-SMNPs, pure 160/66-n CS-SMNPs, and ixed 160/36-n & 160/66-n CS-SMNPs. fig. S5. TEM iages of he inner srucure of supraballs of binary CS-SMNPs. (A 160/0-n & 160/36-n CS-SMNPs, (B 160/0-n & 160/66-n CS-SMNPs, and (C 160/36-n & 160/66-n CS-SMNPs. Scale, 500 n

13 fig. S6. Noral reflecance specra of supraballs ade fro 160/66- and 160/36-n CS-SMNPs, and supraballs ade by ixing differen raios of 160/66- and 160/36-n CS-SMNPs.

14 fig. S7. Calculaions of inverse of noralized ranspor ean free pah as a funcion of differen ixing raios of 160/36- and 160/66-n CS-SMNPs using he scaering heory oulined in SI. (A Shor-range order was aken ino accoun. (B We used independen scaering approxiaion wihou including he odel for shor-range order. The legend represens he ixing ass raios of wo sizes of CS-SMNPs. fig. S8. Iage of a drop of waer on an OTS-coaed glass.