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I am a bit confused and need a well rounded explanation. Have a look at two scenarios:

  • A metal plate with small scratches on it appears diffuse in the optical spectrum, because the roughness reflects the light in different directions. In the infrared you don't see these scratches, because they are much smaller than the wavelength and thus the scratches have very little effect on the reflection direction. Or emissivity if you will.
  • If you have seen nanoporous gold or gold nanoparticles in solution they appear black. The particles are much smaller than the wavelength (<50nm). If you roughen up a surface, the emissivity/absorptivity increases, because the light gets reflected multiple times reducing the amount of light coming back.

So I have two real phenomenons, but their explanations don't fit together. What am I missing?

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  • $\begingroup$ I think that if you conside that objects as small as molecule or ions can have colour you are probably able to solve your dilemma. Don't equate optics from surfaces to absorption phenomena in a sample. Sometimes even a rough out of scale sketch helps. Even if you keep to treat the nanoparticles as nanomirrors, what will happen to a ray entering a multitude of them? $\endgroup$
    – Alchimista
    Jul 17, 2020 at 11:26
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    $\begingroup$ @Alchimista I, for one, don't know what you are getting at here. $\endgroup$
    – garyp
    Jul 17, 2020 at 11:31
  • $\begingroup$ @garyp OP is just treating reflection and absorption on the same basis. The fact that a particle is smaller than the wavelength it dies not mean anything on its "inner" electronic transition. Else no dye would exist. Nanoparticles happen to be in the middle depending on their size. The two supposedly conflicting explanation do not need to fit because the underlying transitions are of different nature. One thing is spectroscopy of a metal bar, one thing is spectroscopy on the same metal ion in solution,to see what we are speaking about. Nanoparticles can have their own absorption spectrum! $\endgroup$
    – Alchimista
    Jul 22, 2020 at 7:06
  • $\begingroup$ Or see it like this. IR does not see scratches. But IR can go as small as a bond vibration. It is the underlying mechanism that matters rather than length. $\endgroup$
    – Alchimista
    Jul 22, 2020 at 7:14
  • $\begingroup$ @Alchimista I don't mean to be rude, but you are writing in riddles. You should post an answer where you explain what mechanisms do play a role if it's not the size. I would genuinely be interest in what you would have to say, since you seem to have a completely different opinion to that of Void. $\endgroup$
    – GRASBOCK
    Jul 22, 2020 at 8:07

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You have the right intuition that light will interact with different structures based on their scale. Specifically, if a structure is much smaller than the light wavelength, the light will effectively smooth it out and ignore it. This is exactly the case of the scratches on the metal surface.

However, this will also happen for light passing around particles; if the particles are much smaller than its wavelength, it will ignore it or effectively interact with the "smoothed out" bulk. If, on the other hand, the size of the particle is comparable to the light's wavelength, it will interact, most likely absorbing the light. It turns out there are even companies that produce golden nanoparticles of various sizes to achieve different colors:

enter image description here

The point of these colors is that light of roughly the wavelength of the size of the particles gets absorbed, light of shorter wavelength gets diffused, and light of longer wavelengths sees the "smoothed out surface" and gets either neatly reflected or passes through.

Now to your example of black nanoparticles. The previous example corresponds to round nanoparticles, that is, particles that do not have any substructure. However, if you make a particle of a more complex shape involving more than one length-scale, such as the spike-balls below, they will absorb light of a broader range of wavelengths and thus a more "black-like" color. enter image description here

From what I have read, a golden nanoparticle solution will degrade over time and the particles will get stuck together (aggregate). Various combinations of the aggregate particles provide various obstacles for light of various wavelengths and thus absorption of a broad spectrum. Broad-spectrum absorption (in the optical) is exactly what we call "being black".

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  • $\begingroup$ Unfortunately obstacle and absorption isn't the same. $\endgroup$
    – Alchimista
    Jul 22, 2020 at 7:11
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I think your question boils down to: why do subwavelength indentations in a metal surface have little effect on the reflectance, wheras subwavelength metal particles can be highly absorptive?

As for the indentations: you need to distinguish between the depth and the width (or diameter) of the indentations. When the indentations are much more shallow than the wavelength [or more precisely, $\ll \lambda/(4\pi)$], they will not scatter much, never mind absorb much. For the diameter of the indentations, it works differently. It is very well possible that shallow indentations with steep side walls and subwavelength diameters affect the reflectance. Radiation (light) is essentially reflected from a metallic surface due to an oscillating electrical current that flows parallel to the surface and mostly parallel to the electric field of the radiation. Steep walls of indentations affect how this current can flow and will therefore also affect the reflectance.

For nanoparticles in suspension, such a current is not possible because the current cannot continue past the end of the particle. That's why small particles don't reflect.

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You‘re not missing anything, because the 2nd explanation about nanoparticles isn‘t really correct. It‘s a quantum effect whereas the first part is classical electrodynamics.

The phenomenon is called Localized Surface Plasmon Resonance (LSPR). It essentially results in absorption, in the case broad band probably due to a distribution of sizes. In void‘s picture the colors correspond to specific sizes.

In a nutshell: a plasmon is a charge (quasi) particle oscillation. In the case of light reflecting at an interface between a dielectric (e.g., like your liquid) & a metal,the SPR is excited in the metal and confined to the surface.

Gold nanoparticles suspended colloidally (like yours) are so small, that part of the surface fulfill the conditions for SPR regardless of the light direction. The size of the particle strongly influences the color.

The stained glass window in the Notre-Dame cathedral in Paris uses this effect for some colors.

If you‘re really interested check out this review paper: doi: 10.1088/1361-648X/aa60f3.

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