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Disclaimer: I am not a professional 3D printer, so I'm not really familiar with how 3D printing works.

I was thinking about trying to make a real life model of the atomic orbitals, to clearly see how the orbitals are really shaped. I thought about trying to 3D print a block, made up of colored transparent "ink", in such a way that the darkness of the color at a point in the block should be proportional to the ψ2 value (probability of the electron cloud). This would print a block in which high density areas are darker than light intensity areas.

My question is, would it be possible to design an algorithm to print a specific darkness of ink at a specific location based on the computed value of ψ2, which is obtained by solving Schrödinger's Equation. Also, would it be possible to have this fullfilled at a reasonable price to be afforded by a regular customer, such as an engineering employee?

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  • $\begingroup$ In line with the answers provided, I'd suggest creating a 3-d plot (on a 2D piece of paper!) with shading as desired. That should be reasonably straighforward in Mathematica or R or python, with some calls to GnuPlot. $\endgroup$ Oct 31 '17 at 18:35
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As Darth pixel mentioned, your best bet would likely be to explore subsurface laser engraving which makes little bubbles inside acrylic to make it translucent (frosted) on the inside in certain places. However, it is expensive, it has no colors, and the resolution isn't usually great (it may look speckled on the edges instead of having a smooth gradient from clear to whitish).

A better option might be to 3d print a probability map of a 2D image an orbital cloud where height corresponds to probability rather than color. (So it will look like a hill or group of hills) This would only run you a few dollars.

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problem definition

I'm not quite sure if it's really question for this group. Looks like the problem itself is more for programming or physics group. Having requested calculations (electron cloud shape) resolved, there will be something to print but...

printing probability cloud

at first, please take a look for example here

it's a review of 3d printing technologies. i think you should have clear picture if your idea is feasible or not.

IMO it's not with todays technologies. in general (and deadly simlified) we have 3 main printing technics

  • out of solid (or semi-solid) filaments - can be colorful and semi-transparent but it's not homogenous in terms of your needs
  • out of solid powders - can be colorful but it cannot be transparent
  • out of liquids - can be really transparent and color but unfortunately not colorful

i'd say rendering but not printing is what you really need

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  • $\begingroup$ Basically, I want to make an probability density model for like a show-and-tell use, while teaching. It would be great to have an accurately made one rather than drawing a crude shape on the blackboard. Once completed, it should resemble a transparent "glass-like" cubical block, in which certain cubic pixels are colored orange, and the intensity of orangeness depends on the ψ<sup>2</sup> value of the Schrödinger wave equation. $\endgroup$ Oct 31 '17 at 9:53
  • $\begingroup$ ... Once completed, the model can be rotated around, and the probability density can be easily visualized, due to the transparent nature of the ink. $\endgroup$ Oct 31 '17 at 9:55
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    $\begingroup$ as mentioned in my answer - AFAIK not possible today. it's possible with a block of acrylic and laser, fluffing the inside... but it sill won't be colorful $\endgroup$ Oct 31 '17 at 10:00
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3d printing a gradient like that will take:

1) A program capable of graphing color into your 3D model 2) A 3D printer capable of printing multiple colors (multi nozzle 3D printers) 3) Some way to convert that density function to a change in color.

There are certain types of files called .3mf files that can hold different color information- but I thinking relating the electron density to a change in color may be rather difficult (if possible at all).

I think a better bet is to go with the 3D probability map of a 2D Image, as suggested by Gumbo.

I have come across a neat little project that is half of what you are looking for. These are mathematically accurate, 3D printed atomic orbitals (graphed with their Schrodinger Equations). Link Here: https://pubs.acs.org/doi/abs/10.1021/acs.jchemed.6b00293

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I suggest you look into Polysher: http://www.polymaker.com/shop/polysmoothpolysher/ and e3D cyclops extruder https://e3d-online.com/Cyclops you can make gradients of color.

But there might even be a smarter way to do alpha transparency than 100% infill with a transparent material:

1) making a lattice of opaque material nodes (where bigger or closer together nodes mean more probability), and using air as the transparent medium

2) dunking the 1) in resin

3) making the afore-mentioned lattice with a partially transparent material and dunking it in a resin of the same refractive index as the transparent material.

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