关于纸沾油后更透明的合理解释，全英文，未翻译。

continuewave · 发表于 2008-4-3 10:34:06

The question was asked:

Why can the transmission of light (intensity) be greater through oil-soaked paper than through the same paper dry? Pioneer settlers in the midwest were said to use oil or lard-soaked paper sheets as windows, they shed rain, blocked the wind, but also transmitted light.
That’s a good one. Actually, let’s start by addressing the exact opposite question:

Given a white piece of paper with a translucent oil spot on it, the most important thing is to understand why the paper is white! Once you understand that, the other question is easy.

What is the definition of white? What is the physics of white? How do you make white? Why are clouds white? Why is the white screen in a movie theater proverbially called the Silver Screen?

Let’s start with something that isn’t white. A piece of pure crystalline quartz is highly transparent. It does not absorb light. It does have an index of refraction. A light beam will partially reflect off the air/quartz interface due to the index mismatch. If you take a zillion identical small quartz spheres and arrange them in a regular lattice like a crystal, you might think that all those little reflections would add up to make something quite non-transparent, but in fact a funny thing happens. If the lattice really is perfect, the scattering is coherent. The coherent forward scattering reconstructs the incoming wave perfectly, making the lattice transparent (although it has a refractive index of its own). You can visualize this in terms of the Huygens construction if you want. For more on this see The Feynman Lectures on Physics volume III chapter 13, or any solid-state physics text.

If, however, the lattice is not quite perfect, an interesting thing happens, called localization. If the locations are exact, but the scattering parameters (e.g. size) is variable from site to site, then we get Mott localization. If the sizes are uniform but the locations are randomized, we get Anderson localization. See reference 1. We still have forward scattering, but it is no longer coherent forward scattering. If you try to do a Huygens construction but randomize the phases of the contributions, you get nothing. More quantitatively, the forward wave is exponentially attenuated with a length scale that depends on the amount of random scattering.

So what happens to all the light that can’t go forward, and can’t be absorbed? It rattles around for a while and then gets tossed out the front surface of our lattice of scatterers. The outgoing light has a wide distribution of angles. Our lattice looks white.

It should be emphasized that the individual fibers in a piece of paper are not white. They are beautifully transparent. It is only a moderately thick collection of randomly-arranged fibers that is white.

Note that you cannot make paper (or paint) that is really thin and really white.

We are now in a position answer the original questions about pioneer windows:

The paper sheds rain because oil is hydrophobic and insoluble. The oil protects the paper from the water.
The paper blocks the wind because paper is strong.
The paper transmits light because oil permeates the pores of the paper and index matches to the cellulose. We no longer have a random array of index-changes. We a thin sheet of relatively uniform index, and the light just waltzes through.
You don’t get perfect transparency for various reasons: (1) Typical oil isn’t a perfect match for cellulose. (2) Typical paper contains not just cellulose but other junk. If you match to one, you can’t match to the other. (3) What’s worse is that the cellulose fibers are hollow and it is nearly impossible to get oil into the cores. Therefore there will always be some scattering off the cores. If we could lay hands on some paper made of randomly-arranged solid fibers (such as rayon, which is solid cellulose), I predict the oil-spot effect would be really spectacular.

不得不佩服老外的科学精神。

关于纸沾油后更透明的合理解释，全英文，未翻译。

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