2.2. Observation of structural color of crystal structure
The structure which we make is a colloid crystal. This is made of three-dimensional periodically positioned particles. This structure can be assumed to be a structure which is composed of stacked up particle layers at regular intervals. The plane made of particle layer is called lattice plane. When we irradiate a light to such periodic structure, the light is reflected by a group of lattice plane. The light reflected by two adjoining planes has different length optical path. If this optical difference are equal to integral multiples of a wavelength of the reflected light, constructive interference is observed at the reflected direction. This interference condition is expressed by Bragg's law
Where m is an integer, λ is the wavelength of the light, n is the refractive index, d is the spacing between the planes in the particle lattice, and θis the angle between the ray of the light and the reflecting planes. The Structural color is an observed result of this interference. In our case, we assume n as a refractive index of the buffer fills around the particle and try to meet this law in a condition of m=1.By this law, we calculate that we need to make d bigger than 150nm to show the structural color with a visible wavelength. Our gold nanoparticle’s diameter is 50nm, so we need to make "linker-SC" longer than 100nm to meet the calculated d. Therefore, we designed "linker-SC" with a parameter k=4.