Fragmented thoughts on Molecular Packing in miniature devices - Page 1
Forum section: electronics / general

author: RJSV
author_rank: Super Contributor
timestamp: June 28, 2024, 09:21:56 pm
content: If you could take a few seconds to view the enclosed photo, a casual gaze shows some important aspects, of modern molecular physics, in miniature electronic devices.It's only a tiny bit of curiosity, sorry about that part...But, as with many folks, I don't have the luxury to engage in only one subject, as pure academia.In the photo, you can realize, for building a 3-D enclosure, the side walls are almost pure OVALS, but the bottom 'plate' must then accommodate the round shapes, by having a very 'pointy' characteristic.While many folks, in electronics technology, choose some obvious path, like circuit design, many are involved on a more basic molecular physics level.Considering the designs, of a cube-like box, I mused that there likely could be a numerical gauge, of the type. Oval type with no sharp points, and accommodating bottom having a shape that's really quite 'pointy'.Circles can get packing, by offsetting each row. A couple of EEVBLOG members refer to the molecular packing geometry, and it's not trivial:Nominal Animal, and Rick Law have this expertise, mentioning 'Face centered' lattice constant (0.543 nm) with molecular details of only 25 or so atoms.I'm thinking; by use of square shaped, you can pack things (atoms in this discussion), pack things perfectly. But atoms, modeled in other shapes, don't have the luxury.As just maybe a fragment of an idea, I realized that my photo shape, of a common laundry bag, has round oval shaped, that need some pointy members for completion of a whole cube like object. Squares and rectangles get a perfect match, in efficiency of packing. That's of the 2-D shape needed, for building the overall 3D boxToo bad we can't at present, do things to manipulate the basic shapes being packed.And I'd like to know if there are numbers of classification rather than using the crude term 'pointy'.

author: RJSV
author_rank: Super Contributor
timestamp: June 28, 2024, 10:46:56 pm
content: My first point being:The close packing, using OVALS or circles goes too far. The ovals then require some less-smooth member (the bottom plate in photo).So, maybe using squares; the squares are moderately smooth, and moderately not (thus the word pointy). Using all squares, or rectangles puts the ultimate 3D shape into a sort of moderate or median amount of faster changing shapes.That's topology, but I can only express some armchair thoughts.Has anyone read this month edition of SCIENCE Magazine? One article deals with molecular layers, and chemistry-looking words that have, like, 32 letters in them. Very dense reading, but I like to challenge myself.DI-methyl-2378-latetal-chlorophosphate- tri423-w axis. VS.Oxy-chromo+made-thisup-inol-6....yeah, THAT.

author: RJSV
author_rank: Super Contributor
timestamp: June 29, 2024, 04:09:51 am
content: Part of the thoughts here involve a sphere, which can be viewed as occupying each of the 3 axis equally, just as a cube can.So the topology of a cube could be said as having 8 'points' in the object.You can notice, the photo shows a fairly 'sharp' set of points. Going to a cube model, those 8 protruding points involve 90 degree angles, that being more than shown in photo object. Going with this idea, it's clear that a pyramid solid, again in 3D, has sharper points than a cube. That example has 6 points.Going the way, towards more edges, say, 5-sided 'panels, as the 2D elements in a 3D solid enclosure. That solid has more degrees in angles (around the points), and thus somewhat softened 'points'. Thus nearer to sphere (no protruding points).That solid has interesting quality that the upper and bottom panels aren't aligned.This sort of gaming has been explored in much more detail bulk than I can discuss.But it seems much of the tiling discussion tends towards 2D surfaces.So, I'm not prepared to get too much into the territory of tiling a 3D object, tending towards a sphere, but, obviously the sphere example is for the case when the number of sides and points is infinite (at the limit).But, at the same time those tiles are growing in count that character number changes. From pyramid, with large 'pointy' character, up through the shapes to a perfect sphere, where it's clear that elusive number is zero.Maybe only elusive because I don't have a huge expertise in topology.That article in SCIENCE, has a lot of topology involved, being involved with a solar cell construction, for changing light energy into voltage. They discuss things on a molecular level, with, like I said, very complex chemical labels used.It's a union of chemistry, physics, and electric focus. Surface layers of only a couple of atoms in thickness.

author: Nominal Animal
author_rank: Super Contributor
timestamp: June 29, 2024, 03:27:12 pm
content: Quote from: RJSV on June 28, 2024, 09:21:56 pmFace-centered cubic lattice and hexagonal close packed lattice are the densest possible packings of equal-sized spheres in 3D. The fraction of the volume occupied by the spheres is \$\pi/\sqrt{18} \approx 0.74048\$, i.e. the "spiky" shapes between the spheres only occupy about 26% of the total volume.Atoms are not exactly spheres, though: they don't have a well defined "surface" or "radius", because it's the electrons bound to the nucleus that defines the atom size and "shape", and in lattices and molecules some of the outermost ones are shared with other atoms. (If we ignore the outermost electrons, the inner electrons tend to be rather spherically symmetric, so using a sphere as a representation is better than any other shape.)So, it is not really about packing cubes or squares; it's more about packing equal-sized spheres, really.

author: RJSV
author_rank: Super Contributor
timestamp: July 28, 2024, 01:56:09 am
content: The word term I was (fumbling) seeking is 'SOLID', a seemingly trivial term.My opinion, this topic, on atomic scale construction, is at the top, or belongs so. Readers; you see a smattering of topics as I post, but the TOPOLOGY science is really deserving of attention.My 'excuse' being resource issues, so I don't expect somebody to extract clarity....Next; planning to get back to local library, searching on Topology subjects, in pure mathematics section.The term; 'Solid' by the way, is for objects like beverage cans, in terms of 3-axis expression. Some responders here mentioned a bit of what I'm thinking, for very small and deliberately built materials (the promise of nano-materials).It's a really wide open field.'Solids', that's the term I was seeking.Thanks for reading!

author: Nominal Animal
author_rank: Super Contributor
timestamp: July 28, 2024, 05:00:31 am
content: As a very off-tangent suggestion, you might be interested in trying outOpenSCAD. It is a 3D modeling environment based onconstructive solid geometryand a language to define and describe said solid geometry objects. Instead of using mouse to place objects and components, you describe them.It is not aprogramminglanguage per se, even though it has loops, because the entire description is taken as a whole (for one instant). For animations, the entire "code" is interpreted fully again for each frame, just with a different value of variable$t. (Variables starting with$have special meaning, and can be used for setting the detail level et cetera.)TheOpenSCAD Cheat Sheetis very useful; each term is a link to a detailed description.For example,Code:$fa = 10; $fn = 36; // Semi-fine precisionR1 = 20; // Base sphere radiusR2 = 12.5; // Cutting sphere radiusd = 10; // Center-to-center distancedifference () {sphere(r=R1);union () {translate([+d,0,0]) sphere(r=R2);translate([-d,0,0]) sphere(r=R2);translate([0,+d,0]) sphere(r=R2);translate([0,-d,0]) sphere(r=R2);translate([0,0,+d]) sphere(r=R2);translate([0,0,-d]) sphere(r=R2);}}generates this sphere with six spherical cutouts:If you want more details, use e.g.$fn = 2; $fa = 180;but (although preview (F5) will be fast), rendering (F6) will be pretty slow due to the huge number of polygons then.The generated geometry can be exported as STL file, and then for example sliced and printed on a 3D printer.

author: RJSV
author_rank: Super Contributor
timestamp: July 28, 2024, 04:23:29 pm
content: Thanks there.I pondered the newer beer can packages that don't have the big circular opening for each can in a six-pack. Maybe it got changed due to various animals and trash dump sea gulls getting heads tangled in the openings ?The new six-pack binders have a solid disc that grabs and holds each can, and I played around with various folds, to obtain varieties of, err, SOLID. (That's what inventors do....play a lot).Now, the usual beer or beverage can, I've been told, is somewhat inefficient shaped, and for the reason of COOLING, for rapid cooling when needed, as the greater height gives a somewhat larger can surface.Ahh, but does this remain true, at nano-scale where you might only have a few molecules from center, to outside world? It might turn out that with a very low number of molecules, the insulating effect is virtually zero.If that is true, then the conventional beverage can shape doesn't have the 'cooling speed's advantage...We would have to rethink some of the packaging types.Of course, I'm thinking towards electronic devices, and heat transfer, rather than beverage can heat transfer. Construction rules and motivation could be different, (and so have different topology goals).

author: Nominal Animal
author_rank: Super Contributor
timestamp: July 29, 2024, 05:13:19 am
content: Quote from: RJSV on July 28, 2024, 04:23:29 pmSurface properties and bulk properties of most atoms differ radically, so it is not really a valid analogy. (You could think of it as surface atoms and bulk atoms having very different thermal properties, so that the size of the clump alone changes its thermal properties.)(Don't get me started on the properties of water molecules' thermal properties, because that way lies the Mbemba effect and related discussions. In a couple of decades, when the current generation of materials physicists are all dead and buried, they'll note that the thermal properties of individual water moleculesvariesbecause of the internal relationships between the kinetic energy degrees of freedom, with such models perfectly replicating the effects we fight and even deny the existence of, because the reality doesn't fit into the simplistic model we insist on. No, it is not "memory"; it is just variance in some properties due to the kinetic energy distribution inside each water molecule in non-equilibrium situations.)Edit: Oops, the following was garbage due to typos; fixed now.As to the properties of cans, if we model them as cylinders with radius \$r\$ (diameter \$2 r\$) and height \$h\$, volume \$V\$ is$$V = \pi h r^2 \quad \iff \quad h = \frac{V}{\pi r^2}$$and total surface area \$A\$ is$$A = 2 \pi r^2 + \pi 2 r h = 2 \pi r^2 + 2 \pi r h = 2 \pi r^2 + 2 \pi r \frac{V}{\pi r^2} = 2 \pi r^2 + \frac{2 V}{r} = \frac{2 V + 2 \pi r^3}{r}$$The ratio of volume \$V\$ to surface area \$A\$ is$$\frac{V}{A} = \frac{ V }{ \displaystyle \left( \frac{2 V + 2 \pi r^3}{r} \right) } = \frac{ V r }{2 (V + \pi r^3)}$$and it reaches a minimum or maximum value when its derivative is zero:$$\begin{array}{rcrcl}\displaystyle \frac{d}{d r} \frac{V}{A} &=& \displaystyle \frac{-3 \pi V r^3}{2 ( V + \pi r^3 )^2} + \frac{V}{2 ( V + \pi r^3 )} &=& 0 \\\iff &~& \displaystyle \frac{V}{2 ( V + \pi r^3 )} &=& \displaystyle \frac{3 \pi V r^3}{2 ( V + \pi r^3 )^2} \\\iff &~& 1 &=& \displaystyle \frac{3 \pi r^3}{V + \pi r^3} \\\iff &~& \displaystyle V + \pi r^3 &=& \displaystyle 3 \pi r^3 \\\iff &~& \displaystyle V &=& \displaystyle 2 \pi r^3 \\\iff &~& \displaystyle \frac{V}{2 \pi} &=& \displaystyle r^3 \\\iff &~& \displaystyle r &=& \displaystyle \sqrt{\frac{V}{2 \pi}} \\\end{array}$$where \$V / (V + \pi r^3) > 0\$ for the roots we are interested, so we could divide both sides of the equation with it.Substituting \$r = \sqrt{V/(2 \pi)}\$ to \$h = V/(\pi r^2)\$ gives us the optimum height,$$h = \frac{V}{\pi r^2} = \sqrt{ \frac{V^3}{\pi^3} \frac{2^2 \pi^2}{V^2} } = \sqrt{\frac{4 V}{\pi}}$$Thus, the optimum ratio of height to diameter is$$\frac{h}{2 r} = \sqrt{\frac{4 V}{\pi}} \sqrt{\frac{1}{2^3}} \sqrt{\frac{2 \pi}{V}} = \sqrt{\frac{8 \pi V}{8 \pi V}} = 1$$In other words, if you want to minimize the surface area to volume ratio using a cylindrical shape, the diameter should be the same as the height.A typical beverage can here is 330cl = 330 cm³, so their optimum diameter and height would be about 7.5cm.In the real world manufacturing requirements affect the shape, too. The beverage is pumped into the container at quite high rates, so optimizing the pressure durability versus material used matters a lot.As to thermal transfer materials, we have a lot of options that are poorly used. For example in computing, we could use immersion cooling with suitable mineral oils; we already do the same for some power electronics. A simple option is to use passive air cooling with large enough (efficiently shaped) heatsinks, with the heat-generating components (like the CPU or MCU) on the heat sink side of the PCB, and the rest on the other. (I first saw this in commercial products in some SBCs, and was a major reason why I bought myOdroid HC-1.) The idea of usingairas the primary heat transfer medium is just silly. Horizontal fins are near useless without a fan, because hot air rises up. Straight vertical fins are not the most efficient, because laminar flow does not do optimal heat exchange; some turbulent flow would be better. How many people on this planet right now are scientifically examining optimal heat sink fin shape and densityfor passive airflow? 0-10 at most, I'd wager. See?

author: RJSV
author_rank: Super Contributor
timestamp: July 31, 2024, 01:39:12 am
content: Thanks. That's some challenging math and I like reading things that are way more complex, than my own capabilities.When I grabbed the six-pack I found that it was more 'interesting' when folding to make a typical, upright can shape. Too bad I couldn't find that plastic binding piece, with it's six discs.Originally wished, to fold those six connected discs, to make a more perfect shaped cube, (six sided). Of course, the plastic connecting piece, when with height of 2 (discs), you only get 3 sides, needing 4.But you can model the cylinder as 2 units high, and then with 4 sides....(still also ignoring the top and bottom piece).Sorry, I don't mean to be mysterious here; really going to have to fetch my connecting piece, or buy another beverage six-pack, to clearly show what I'm thinking.

author: RJSV
author_rank: Super Contributor
timestamp: July 31, 2024, 03:29:23 pm
content: I'll have to buy some beverage Six-Pack for the package 'binder' mentioned. (I'm often seeking the appropriate technical terms).The cylinder can shape with evenly balanced dimensions, same on all 3 axis, but, interestingly, fitting the 6 disks as walls would require a cut, of the 2 by 3 binder, (2X3 flat).The six pack 'binder' itself lends to being folded as 2 discs high, by 1.That comes out in total, as 4 walls, each 2 high, plus a top and a bottom...total 10 discs to make a cylinder can shape.

author: Nominal Animal
author_rank: Super Contributor
timestamp: July 31, 2024, 05:33:59 pm
content: Note I fixed the math above. I did an image search on six-can cardboard carry-boxes, but there are just so many, I cannot tell which kind you're referring to.So many interesting ones, though!

author: CatalinaWOW
author_rank: Super Contributor
timestamp: July 31, 2024, 06:08:53 pm
content: Sometimes math and reality don't mix well. Using air as a heat transfer medium is silly if you are optimizing on a few simple parameters like density and heat capacity. But for a long time it was good enough, and the reality is that air is going to be somewhere in the thermal path for any piece of portable or even semi-portable piece of equipment. That is changing as CPUs and other components start generating heat (in units of power/volume) at rates that used to only occur in devices that didn't mind being hot. Things like filaments in light bulbs and vacuum tubes. As a result there is much work on optimizing the heat path to the point where the power to surface area ratio is low enough to make it not worth the time or equipment to do better than air for the remainder of the thermal path.And remember that air has some really neat non-thermal properties. It is stocked everywhere on earth and leaks don't matter. And perhaps most importantly there is an incredibly large industrial base making the equipment to move, direct and absorb heat from air. Those advantages of scale are real and hard to model correctly in an optimization equation.

author: RJSV
author_rank: Super Contributor
timestamp: July 31, 2024, 08:35:55 pm
content: The blue colored disks have a lip that is press-fit over each beverage can.That 'bracket' piece binds your 6 pack cans, rather than the old style open in middle, where can top was exposed. My theory that is to avoid wild animal entrapments, at landfills.It was such a an inviting distraction...more interesting to play with, than the original subject...Any folding, to make a cube that's '1 by 1 by 1' will need a couple of cuts, in the flat '3 X 2' bracket. (Still needing a better term).

author: RJSV
author_rank: Super Contributor
timestamp: July 31, 2024, 08:44:19 pm
content: In the meantime, before I can get back to purchase at store; here is photo of the 3-sided out of 4 sides, that the bracket can form, upon folding.While playing around with any possible folding variations, this one is more 'natural', meaning that the flat 3 by 2 bracket seems to almost suggest certain folding options...even if it does actually directly suggest a 3-sided solid, rather than a 4-sided solid.Thanks for reading about my Origami muses!

author: RJSV
author_rank: Super Contributor
timestamp: August 09, 2024, 08:02:34 pm
content: I found the six-pack holder, that, like I've said, does not have the hollow 'ring' shape that can trap wild animal's heads, in a landfill.But I'm into what that part suggests, in doing folding into a 3D 'solid'. Picture here shows the holder flat, as used. But, you can appreciate; with several cuts you will have 2 sections that can merge, into a cube; 1 unit by 1 unit by 1 unit.Next:

author: RJSV
author_rank: Super Contributor
timestamp: August 09, 2024, 08:13:25 pm
content: Next, here you will notice, a more 'natural' folding can make a rectangular 4-sided upright 1 by 1 by 2 units high, or at least 3 of the sides.Idea is that the whole, flat shape would be a nano-scale construction, to be folded.Of course even more 'natural' would be to fold that flat object into a 3 sided 'solid', and without needing to supply a 4th side.No top or bottom piece, in those 2 folded variations.

author: RJSV
author_rank: Super Contributor
timestamp: August 28, 2024, 11:20:07 pm
content: Picture here shows; variations in how you've cut up the 'flat' assembly, in this creative exercise. By cutting the flat '3 by 2' in a zig-zag that gives two pieces, each can consist of one central 'end piece', and that can be assembled, into a typical 6-sided cube as a solid object.

author: RJSV
author_rank: Super Contributor
timestamp: August 28, 2024, 11:39:58 pm
content: Sorry about camera quality, the picture shows how a 'flat' assembly can be cut; in a zig-zag, to create two pieces. Those two 'sub-units' can be folded, resulting in a 'cube' form, for each, and, ultimately, can be assembled into a basic 'cube' shape, having six sides in the resulting SOLID.A similar cut and fold sequence can, alternately, also form a cube. Each half in that case would form a 'U' shaped folding, starting with each half being a straight cut '1 by 3' taken as two pieces in that same starting (flat 3 by 2).

author: RJSV
author_rank: Super Contributor
timestamp: August 28, 2024, 11:54:02 pm
content: I took photo of notebook page to show these two options, where you've started out with the flat assembly, '3 by 2' in this case, (using beverage 'six-pack' plastic binder for store shelves).You can see the second option; making the separation cut, to make a pair of straight lined '1 by 3' for folding. After cut, fold each sub-assembly into a 'U' and nest them together.Much of this might not be directly flowing some 'rules' or commonly used construction, but that's OK here, in casual exploration of various topology that MIGHT later be applicable.Right now, I'm just exploring the topology aspects, using crude geometry (solids).

author: RJSV
author_rank: Super Contributor
timestamp: August 29, 2024, 12:22:21 am
content: (Im using adhesive tape to display the halves that have each been folded.)Picture shows the two halves of cube; each half already expresses a 'six-sided' cube, for completion when the halves are joined, into the SOLID, 6-sided cube.With the theory aspect, I like the way the product itself puts forth a suggestion, of what can be built, as a kind of 'natural' outcome, of the original shape.In the nano-scale, I'm thinking in terms of a 'chemistry flask, containing several millions of the starting shape, (various) and what SOLID can be built, assuming some sort of dissolving process, followed by establishing links, with other compatable items. In this experimental case, it's the flat individual disk, that will become one of the 6 walls of a SOLID cube.Interesting how the object itself seems to have a couple of 'natural' configurations, that can build a cube,....in one or more styles of assembly.In the chemical sense, at nano-scales, those disk shapes might only be something like 9 mecules, each. (I'm not yet speculating on types). Its a bit strange method, of building devices.This is the territory, of inventor's, by the way:It's, much of it, very new and demanding different thinking....(and no fear, of the unknown). Sticking to 'convention' feels safer, lol; needing someone to 'hold my hand', for security....This, is inventor's territory.

author: RJSV
author_rank: Super Contributor
timestamp: August 29, 2024, 12:44:01 am
content: Thanks to adhesive tape, the completed cube looking unstable / imperfect. Even that aspect, I've been paying attention to, as the sort-of natural path forward, in exploring SOLIDs in 3-D.In fact, it's that behavior, having natural and more forced outcomes, that I find even MORE interesting, in a pure science / examination sense. Some SOLIDs, for example, don't keep a proper balance symmetry, in mechanical terms, from gravity. You may have noticed, that in building a SOLID, using 5 sided walls, some upright shapes do not have the centers aligned, of top vs. bottom...and so that object might not be suitable, in structures. (Centers of gravity, differ, between top plate and bottom plate).

author: RJSV
author_rank: Super Contributor
timestamp: August 29, 2024, 01:03:10 am
content: Of course, this speculation exercise owes to previous yt videos, on making nano-sized NERF GUNS, where the chemical bath has the functions, to 'snip' molecules and reassemble into the 'Nerf Gun' shape, starting with a brew of chemicals....similar to DNA based construction.Lol, very distant from traditional pc boards and copper traces.

author: RJSV
author_rank: Super Contributor
timestamp: August 29, 2024, 04:05:06 am
content: Here is a (slightly) better made picture of 6 sided plastic cube.Sorry about the quality issues....Dropped my phone, on cement walkway. With the current economic status, I'm figuring on catching up on some other priorities, September, and MAYBE clear, to replace phone, in OCTOBER, for certain....(cash only needed for food purchase, these days.). Uggh, I hate the poverty because of the many limitations, lacking resources to take care of routine stuff, but also (any) innovation ideas get scuttled....till months pass...takes a disciplined approach !But, still, sorry for image quality, here.