Theoretical condition for transparency in mesoporous layered optical media: Application to switching of hygrochromic coatings

Abstract

Mesoporous Bragg stacks are able to change color upon infiltration or displacement of liquid compounds inside their porous structure. Reversible switching from transparency to coloration offers additional functionality. Based on Bruggeman's effective medium theory, we derive a transparency master equation, which is valid for bilayers of arbitrary host materials and pore-filling compounds. The transparency condition fixes pore volume fractions such that the effective refractive index is homogenized through the bilayer, hence, through arbitrary layered optical media built from this bilayer. This general concept is applied to the case of switching of hygrochromic coatings made of mesoporous mixed oxide Bragg stacks.

Liquid-induced colour change in a beetle: the concept of a photonic cell

“…Recently, part of the development of bioinspired materials has come to rely upon natural porous materials found in living organisms exhibiting properties such as structural coloration 6 7 , hygrochromism 2 5 8 9 , fluorescence 10 11 12 13 14 15 16 17 18 , gas or vapour sensitivity 3 19 20 21 22 , thermal management 23 and/or antireflection 4 24 25 26 27 . Examples of this approach include bioinspired smart coatings 28 29 . In our study, we characterised colour and fluorescence change dynamics induced by various liquids and analysed in detail the chemical composition of the beetle’s scales.…”

Controlled fluorescence in a beetle's photonic structure and its sensitivity to environmentally induced changes

“…Many biological photonic structures are porous and comprise biopolymers such as chitin, keratin, and cellulose. The range of structures and optical effects found in biological systems, which have been optimized through evolution for millions of years, enables the development of new designs and possible technological applications through an approach that incorporates bioinspired principles [16][17][18][19]. Another optical phenomenon found in living organisms is fluorescence emission.…”

Nanostructured Surfaces: Bioinspiration for Transparency, Coloration and Wettability

“…As a result, the calculation is considerably simplified since the corrugation is treated as a stack of planar homogeneous layers of gradually varying effective refractive indexes. The effective permittivity of each layer, ε eff =(n eff ) 2 , can be calculated by Bruggeman's formula applied to air(ε a =1)/chitin(ε c ) mixed medium [7]: ε eff =[g+(g 2 +8ε c ) 1/2 ]/4 with g=(3f-1)ε c -3f+2 (f: air filling fraction). For an array of truncated cones separated by the distance a, the air filling fraction is f(z)=π(r(z)/a) 2 , where r(z) is the local radius of the cone in the layer (depicted as a yellow cylinder in Fig.…”

“…This color-totransparency switching of a biological multilayer has inspired recently the fabrication of hygrochromic mesoporous dielectric multilayer coatings [6]. A rationale for the design of coatings that are switchable from transparency to highly saturated (Bragg) color upon infiltration of liquid in porous multilayer has been theoretically proposed [7]. Much has still to be discovered regarding the interplay of physical properties of natural nanostructures and their use for various biological functions.…”