Revision as of 12:44, 27 August 2017

This is an introduction to the character of robotic work in the nanocosm.
It should deliver some intuitive feeling of how things work down there.

Pluck yourself a Hair and look at it. Imagine a magnified model of the torn of end was built. Would be interesting – wouldn't it? This model was buried halfway such that it runs vertically into ground at the sidelines and that it reaches twenty-five meters of dome-height at the center of the play-field. When you stand on this soccer field in front of the fractured surface and you hold a real hair against tremendous model then you see: The model-atoms of the giant hair have the diameter of a real hair.

How big is an atom?

Atoms are quite small but they are not as ridiculously small as people usually say. If a hair (0.1mm) would be the width of a soccer field (~60m) an atom would be roughly the size of a hair. Carbon is about 0.2nm or 2Å in size that makes roughly five atoms per nanometer. When hierarchically building up building structures one can quickly fill up this size gap.

How does it feel when you grab two atoms and rub them against each other?

Force feedback devices like this one allow one to gain a very intimate understanding of how things behave at the scale of atoms.

First I should note that trying this out for real is actually possible for quite a while now (as unbelievable as it may sound). To feel atoms you grab the end of a robot (you shake hands with it). A tiny needle with a single atom at the tip is then made to move exactly like your hand just on a lot smaller scale. When the topmost atom on the needle tip starts to touch an atom on a surface the robot arm pushes back just as the surface pushes back on the needle albeit with a magnified force big enough for you to conveniently feel it. This is called force feedback (commonly known from car racing games).

Two analogies that might convey what it feels like best are:

• rubbing soft slippery fish or water soaked gummy bears against each other
• moving two magnets past each other in repulsive (but sometimes also attractive) configuration

Moving the robot arm in and outward you can check out softness and moving sideward you can check out slipperiness.

Slipperiness

Atoms are ridiculously slippery. Like the moon orbiting the earth there's basically no friction. If certain conditions are met this low friction can be retained for larger contact areas than just the single atom on the tip of our probing needle. One condition is that the atomic ripples on a touching pair of larger surfaces must not interlock like matching egg-crates. If this and a few other things are met there is extremely low friction. It is called the superlubrication phenomenon and it has enormous potential for technical usage in slide bearings of all kinds.

Softness

So how does it feel to break a single bond between two atoms? Since I can't let you pull on this robot arm over the web lets turn the robot arm facing downwards and tie an empty plastic bottle onto it in which we will later fill some water. We can also use a simple coil spring instead of the robot arm giving force feedback

For realism we can make the robot arm behave exactly as stiff as the bond between two atoms. Caution! Please do not mistake stiffness with force. Stiffness is how much the force grows per the length you pull. A bond between two atoms obviously has only a tiny force but this force builds up on a tiny distance. Thus while the robot arm needs to magnify both force and length the stiffness of the bond turns out to be in the right size such that the robot arm can simulate it 1:1.

Now here's a quiz: Assuming you fill half a liter of water into the plastic bottle how much will the robot arm simulating the stiffness of a bond between two carbon atoms in diamond give (very roughly)
A:~1mm ☐ B:~1cm ☐ C:~1dm ☐

How do atoms work?

The common symbolic depiction of atoms with lines for orbits and little balls on those lines for electrons and further little balls for the protons and neutrons in the core is awfully bad and very far from the real situation. A decent intuitive picture for atoms are soft/blurry clouds that are as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp orbits. These clouds are made of so called "electron density". Atoms basically are electrons. The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.

Side note 1: Electrons in solids can be bigger than atoms. As an example: Free electrons in metals are of such nature.
Side note 2: Electrons in atoms (of internal origin) can not be smaller than the innermost electron shell. Otherwise one talks about the existing "virtual energy fluctuations" of electrons (not to confuse with virtual matter antimatter particle pairs). If electrons in atoms would really be smaller than the innermost electron shell they would need to have so much impulse and kinetic energy that they would leave the atom promptly. (Technical details: Impulse too is a blurry cloud. The mentioned "high impulse" here actually means a broad cloud in "impulse space". The seesaw that makes tightly constrained electrons move more vigorously is called the "Heisenberg uncertainty relationship")

The very small core/nucleus of the atom (which btw is also cloudy but more rowdy - excuse the joke) just serves as a very well hidden glue holding the electron cloud together. The inner electrons serve as padding. They shift some electrons further outward (due to the Pauli exclusion principle) making them the outer electrons. Only due to this outward shifting the clouds outermost exposed electrons undergo interesting changes that make chemical bonds possible.

What kind of interesting changes? As a first crude starting analogy imagine the electron density (actually a precursor of it) as the skin on a drum. The lowest tone you can play makes the whole membrane go up and down (a single antinode of vibration).

There are several points where the useful drum analogy breaks and some awkward peculiarities show up:

• The membrane has no border – (again: there are no sharp surfaces).
• The tension of the membrane changes towards the center.
• The membrane is not two dimensional but three dimensional and it does not swing up and down but into a further dimension that is the precursor of electron density. This precursor can be best expressed with complex numbers and is called the "wave function" of the electron.
• Every tone can be played at exactly one volume.
• Every tone can be played exactly twice (spin up and spin down) then if one wants to play more tones one needs to go on to the tone next higher in frequency/pitch or to a tone different in geometry. (This is due to the Pauli exclusion principle.)
• Tones do not radiate away energy. They do not emit the equivalent of the drum-analogy-soundwaves in form of lightwaves. Instead they stay at their frequency pitch permanently unless actively driven away. Electrons don't "fall" into the core due to the seesaw that makes electrons move more vigorously when they become tightly constrained in space. The "heisenberg uncertainty relationship".
• The overtone vibration geometries have inter-dependencies (more on that later).

Exactly two electrons go into the very first tone (the two spins - spin up and spin down - then this place is full - Pauli exclusion). The next higher tone of the drum (aka the first overtone) has the inner circular area of the drum going up-then-down and the outer circular ring-area going down-then-up. In the 2D drum model a motionless circular "nodal line of vibration" is located between the two "antinodes of vibration". In the real 3D atom this "node of vibration" is a infinitely sharp spherical shell with the inner and outer volume separated by this shell swinging complementary to each other (in antiphase).

Technical side-notes: The number of nodes can further rise and directly corresponds to the strain and energy in the "drum membrane" (curvature in the wave function). With every additional node one is raising up one energy level. These energy levels are characterized by the "main/principal quantum number" with symbol "n". Numbers of n have associated letters (0=k 1=l 2=m ...).

There are overtones with non-spherical nodal surfaces too. In the 2D drum model imagine the left side of the drum going up-then-down and the right side going down-then-up. It's a bit more complicated in 3D atoms though.

• There are nodal surfaces that have the shape of nested double cones (and one plane in case of even node-surface numbers) dividing the wave function in one double lobe and some rings. (Rings only if there's more than one node-surface.)
• There are nodal surfaces that are all flat planes which divide the wave function into orange slice shaped antinodes.

The former is described by the "secondary quantum number" with symbol "l". Again numbers of l have associated letters (1=s 2=p 3=d 4=f). The latter is described by the "magnetic quantum number" with symbol "m"

Due to the fact that the wave functions are a result of a certain very famous differential equation there are some relations between those so called "quantum numbers". These relations are: (n>0; l<n; abs(m)<=l). In words: higher overtones (vibrational modes) of different kind than spherical only become available when the energy rises above the minimum (n>1).

Note that when n becomes 2 then l can be lifted from 0 to 1. This lifting drags the spherical/radial node-surface over to a conical node-surface. The spherical node-surface is gone (kind of like a conversion). Also one can further "lift" m form 0 to minus 1 or plus 1. This further drags the conical node-surfaces over to a planar node (again kind of like a conversion). Now the conical node is gone too. With higher n one can leave some spherical/radial node-surfaces behind albeit converting some to the conical type and one can leave some conical ones behind albeit converting some to the planar type. This allows for complex patterns (technical term "spherical harmonics"). We are especially interested in the volume-slivers between the node-surfaces. These are the basis for orbitals bonds and the shape of molecules. But we are not quite there yet.

Technical side-note: There are the so called "Hund's rules" describing in which order electrons fill up the quantum numbers. This though applies only for unbond atoms that freely float in vacuum (E.g. found in vaporized metals in gas discharge lamps. Lamps that where and still are very useful in fundamental physics.) Since we are mostly interested strongly bonded atoms here these rules are not useful as they are. Instead the described vibrational modes of the wave function combine in more or less nontrivial ways to bonding orbitals such that energy is minimized.

What kind of shape do atoms have?

Now with the somewhat intuitive drum analogy for the oscillating wave function and the vibrational overtones of the wave function which are dividing atoms into kind of a 3D checkerboard pattern (spherical harmonics) we are slowly beginning to get some structure that we'll need to form directed chemical bonds.

Our goal is to get directed lobes (bonding electron orbitals) from the nodes in the wave function but there is another not yet mentioned peculiarity which makes getting bonding orbitals from the basic patterns more difficult for us.

The problem is that electrons can not only oscillate they can also rotate (since there's no angular constraint - no "wall" in the atom). The density of a moving/streaming/rotating one electron cloud (both linear and like in our case circular) features no nodes. This is because:

• The precursor of the electron density(the wave function) has its purely complex part phase shifted relative to the purely real part in the direction of movement - (TODO: check sign). Side-note: From the shift in the wave function one can derive the direction of motion even when given only a momentary snapshot, so the shift can be seen as the encoding of the motion, the motion is the shift, one and the same.
• The density of the electron cloud is obtained from the wave function by forming the "square of the absolute value".
• The resulting density of this moving phase shifted wave functions is constant and nowhere zero.

So none of the nodes and antinodes of the wave function make it over to the electron density. We don't get the desired patterns of slivers between nodes-surfaces that are bonding orbitals.

Side-note: Despite the many vibrational node-surfaces, free atoms that are floating around in a vacuum (and that are not under the influence of magnetic or electric fields) have the shape of perfect spheres when the wave function is converted to observable electron density. This is exactly because they have no rotational constraints. (Related: symmetry <=> conserved quantity == Nöther theorem)

To get patterns one can reflect back a one electron stream on a wall into itself or as in our case we can add fractions of the one electron stream rotating backwards (this is a quantum superposition btw) some parts of the wave function cancel out (self interference) and after applying the "square of the absolute value" to get our (observable) electron density we finally get lobes (we have standing waves).

Looking backward when one has (at least one) chemical bond to something non rotation (e.g. a macroscale slab of crystal) this bond could be seen as the aforementioned "wall in the atom" that prevents rotation.

To minimize energy furthermore the basic wave functions are combined in such a way that energy is minimized (metastability not considered here). From that one gets various combinations of basic orbitals which are called "hybrid orbitals". The most important hybrid orbitals for the lighter elements are the called sp³ and sp². There's also the more rare sp hybridization.

sp³ orbitals

sp³ hybridization results in four strongly asymmetric double lobes oriented in tetrahedral geometry. The shape of coastal defense tetrapods. The small sides of the lobes are hidden away in the atoms inner shells.

The orbitals of atoms facing one another bond big lobe facing big lobe. These bonds are so called "sigma bonds". A classic example for a solid material featuring sp³ bonding is diamond. Note that one needs at least four bonds not lying in a common plane such that one can create densely meshed 3D structures that are not just folded chains or sheets. A classic example for a volatile compound featuring sp³ bonding is methane CH₄

sp² orbitals

sp² hybridization leaves one p orbital (p_z) intact (as it is) the remaining three are converted in asymmetric double lobes (less strongly asymmetric than sp³). The small sides of the lobes are hidden away in the atoms inner shells. The remnant symmetric p_z orbital is oriented vertically while the three sp² orbitals lie in a normal plane forming an equilateral triangle.

The hybridized orbitals form again form sigma bonds. Actually the unaltered p_z orbital are more interesting here. Double lobes bond sideways to other double lobes making single bonds with two contact points so called "pi bonds". A classic example for sp² bonding is: graphite, nanotubes, buckyballs, ...
Depending on bonding topology and lattice strain the electronic properties of these pi bonds can be tuned in a very wide range. From metallic over semi-metallic to non metallic.

Note that bigger atoms like silicon (sitting below carbon in the periodic table and thus similar) rarely form sp² or even sp bonds. It's not impossible but very unstable. The inner electrons are in the way.

sp orbitals

sp hybridization leaves two p like orbitals intact (rotation compensated - as noted above) the remaining two are converted in asymmetric double lobes (less strongly asymmetric than sp2). The small sides of the lobes are hidden away in the atoms inner shells. The two remnant symmetric p like orbitals are oriented normal to each other while the two sp orbitals stick out on opposite sides of the formed cross. Attention! these two can be mistaken for a unmodified p orbital.

sp hybridization occurs in the gaseous compound ethyne (C₂H₂) aka acetylene aka welding gas. This gas is of especial interest for advanced mechanosynthesis of diamond because a triple bond between two carbon atoms leaves just two bonds capped with hydrogen. When assembling something like a block of diamond instead of hydrocarbon chains there is very little surface area and all that excessive hydrogen would need to be reacted to water leading to a massive energy excess.

d orbitals and their hybridization

• TODO ...

Speeds of motion in nanorobotics

Today it's general education that temperature is equivalent to the speed of motion of particles at the atomic scale. If you unfamiliar with this "thermal motion" also known as "brownian motion" I suggest you read up on this elsewhere (e.g. wikipedia) before continuing here.

The incredible rate things zap past their surroundings (just driven by temperature)

Thermal motion at the nanoscale is pretty incredible.
Small single molecules zip around at thermal speeds of a few hundred meters per second. That's about the speed of sound. When we scale up size by our usual magnification factor of 500.000 to make model atoms (say water molecules) have the diameter of a human hair and when we keep the flow of time unchanged then those hair sized molecules zip around with more than half the speed of light.

But since those water molecules are densely packed they do not move in long straight lines.

• In liquid phase (e.g. water) they move in twisty paths with curve radii of about their own size.
• In one atmosphere gas phase (e.g. air) they move about 250 times their size (the mean free path length) before colliding and making a more or less U turn. In the 500,000 times scaled up model those U-turns are executed at near the speed of light every 2.5 centimeters (250 x 0.1mm).

Note that molecules in a liquid or gas that are not bond to a crystal run apart quantum-blurrily quite quickly (more on that later). So a "soup" of a superposition of all possible collision-histories is a better picture for fluids and gasses.

Assembly by mindlessly throwing parts together at ridiculous rates

Given this situation it becomes very obvious that in a liquid environment that is densely packed with other solvent molecules (e.g. water) solvated molecules meet a lot of other solvated molecules in a very short amount of time. Bigger more massive molecules like proteins ("puzzle piece molecules") move slower but collision rates are still very very high.

This is why puzzle piece shaped proteins molecules in biological systems can "assemble themselves" into their intended products. Via their random collisions they just mindlessly try all possible places they could bond to in very very fast succession. It's mindless trying like having toddlers that do not yet grasp that cubes do not fit through round holes do the assembly job but since it's done so fast (like brute force computer algorithms) useful things can be assembled nonetheless.

The technical term for this method of assembly is "self assembly" but here we'll call it "thermally driven assembly" which captures the meaning better. On the day to day macroscale this method of assembly is usually not applied for practical purposes due to its ridiculous slowness and requirement of parts fitting together like a sticky puzzle. Fully grasping the process how it happens at the nanoscale at an intuitive level may be impossible due to the vast number of trials until the final successful bonding reaction. (TODO: investigate better visualization methods) There are beautiful CG videos of molecular biology that use fake motions mo make it comprehensible (TODO: add link).

Use of thermally driven assembly to get away from thermally driven assembly ASAP

Thermally driven assembly is the predominant form of assembly in biological systems. Thermally driven assembly of increasingly arfificial molecules will be (and already is!!) a very useful tool for walking the initial steps of the path to advanced nanofactories. But as it turns out in an advanced nanofactory (the far term goal) it makes much more sense to actually constrain / suppress thermal vibrations and take care of the transport oneself in a fully controlled and less mindless fashion.

The idea of working towards a point where we deny the help of thermal motion (shunning the teachings of nature) but doing assembly tightly controlled and guided instead has received harsh criticism in the past. It was and still is often misunderstood as a misunderstading of the real nature of the nanocosm.

But there actually is an example where we already succeeded with the suppression of thermal noise. Nanoelectronics. In microchips we've already learned to suppress thermally caused electrical noise without even noticing it since it just gradually got more difficult.

The two necessary requirements for thermal noise suppression are the same that we used to get away from analog technology namely:

• error margins and
• error correction

Now we use mostly digital electronics.

Given that electrons start to behave strongly quantum-mechanically in the nanoscale (quantum blurriness and thermal motion can often be treated in a common fashion) -- which stands is in stark contrast to nanomechanical nanomachines -- this is even more of a feat. We where not forced to switch some sort of probabilistic electronics (whatever that would be). Since much less quantum mechanical in behavior advanced nanomechanical systems will have even less reason to work in a purely probabilistic fashion.

The smaller the more productive

Main article: "Higher productivity of smaller machinery"

While size goes down speed goes up. A good example in nature is the increasing wing flapping rate seen in birds and insects.

By naively scaling down a current day 3D-printer by a factor of 500.000 (just for illustration - not a serious proposal) it becomes 500.000 times faster. A typically time for 3D printers to print parts that have about the mass of the printer itself is on the order of 10 hours. This shrinks down to just 0.72 seconds.

Now a single shrunk down printer won't produce much but imagine the whole volume of the original non-shrunk printer filled up with shrunk down printers. This would then produce the macroscale printers own mass in less than a second.

In a serious advanced nanofactory design the time to produce the production machinery's own mass can become even smaller due to better materials, lower friction, smaller size steps, to name a few reasons. For a good intuitive feel about the production rate imagine products shooting out like rifle bullets.

I fact the time to produce production machinery's own mass can become so short that the products that can be produced at the nanoscale cannot be fed out fast enough at the macroscale anymore. Getting even remotely near there would require impractical levels of cooling.

Solution: One humbly accepts not to get the full crazy level potential of nanoscale production machinery and is content with just more than practical levels of productivity.

To do this one does not fill up the whole volume with productive nanosystems. One abandons the concept of clouds of molecular assemblers. Instead one integrates everything in a thin chip. A nanofactory. For details check the main article: Macroscale slowness bottleneck

Even in the case when one really wants to push the limits (there's likely military interest here) its likely that a highly advanced fractal nanofactory that is a little thicker is the best solution. For a continuously running device the cooling facilities then are likely much bigger than the productive device itself. The production becomes highly inefficient and turns a lot of energy into heat. Still there is the fundamental specific acceleration limit which cannot be exceeded. This is the point where no known material would not break from the acceleration loads.

Motions in the far term goal of advanced nanofactories

Assembly in an advanced nanofactory will resemble more of a factory assembly line far away from any similarity to biological systems. All the machinery will usually run much slower than the thermal motions (about at least a factor of 1000) but since every try is a hit (for all practical purposes) the production throughput can be the same or higher than the one of natural bio-systems that work with thermally driven assembly.

In rare occasions one might want to let go of molecules or crystolecules in an advanced nanosystem. Thermal motion for bigger crystolecules in a vacuum under gravity are statistically distributed throwing parabolas. Single molecules show significant quantum blurring when released.

• Envelope of throwing trajectories with same speed
• Throwing trajectories with various speed in same direction

What happens when you let go of a building block?

Let's consider an somewhat unusual fall experiment. A small gripper let go of a building block. Simple? See if you answer right.

A fall experiment quiz to illustrate the quite unfamiliar mechanical behavior in the nanoscale.

Scaling laws

They describe what changes when one goes down the scale. E.g. that magnetic motors become weak but electrostatic ones strong. More details can be found at the scaling laws main page.

The feel of AP Products

AP products though robotic and gemstone like in the nanocosm are not necessarily cold hard and robot like to the human senses. Emulated elasticity can create any form imaginable with gradients from soft to hard. It isn't an easy to attain property but it is an highly desirable one and will emerge at some point.

Bonding energies - Tensile strengths - Stiffnesses

(TODO: Add the same info table as on VdW force page)
[Todo: Add table - make it visualizable for covalent bonds and VdW bonds]
[Todo: show surface area thats VdW ashesion is energetically equivalent to one covalent bond - related: Form locking]

• Connection method#Van der Waals locking
• Van der Waals force

Further

• Periodic table of elements
• acceleration limits
• jumping building blocks
• Why nanomechanics is barely mechanical quantummechanics
• Video Playlist: The Shape of Atoms and Bonds (By "Learn Hub")
• Distorted visualisation methods for convergent assembly
• Scaling laws