> how they "feel" the interactions without disturbing them
They can't. I don't know if there are quantum complications at that scale that change this picture, but my basic idea from classical physics is that Newton's Third Law says the probe can't have a force exerted on it by the sample (action) without also simultaneously itself exerting a force on the sample (reaction).
> The single-atom moving finger of the nc-AFM
The mass of the detector particle being deflected by the fields is small compared to the mass of the molecule being measured. So a force large enough to move the probe by a lot might still be small enough to only move the sample by a little.
The bottom line is, you can't measure a sample without disturbing it, but as the ratio of probe mass to sample mass shrinks, the level of that disturbance also shrinks. In this case they're using a single atom probe to measure a large organic molecule, apparently the ratio is small enough.
> Resulting movements of the stylus are detected by a laser beam
I guess in order to engineer a system this small, you need a probe to measure the probe. Again I'm guessing the momentum of the photons from the laser that are used to measure the probe atom is small enough not to appreciably deflect the probe.
Nitpicking, but just going with classical physics and Newton's Third Law, yes, you can do such things. If the thing you're studying emits something, and you can infer the thing's state from what it emits, you can study the emissions without disturbing the thing. Similarly, looking at something doesn't change its state, since the light was already reflected / emitted.
Obviously there are additional complications at such small scales, and it depends on what you're detecting (measuring / passing through magnetic fields does affect the source since it changes the field), and it depends on what you define as "change" and which quantum mechanics interpretation you subscribe to. I'm just pointing out that the thing being measured doesn't have to be the thing you're investigating, so that law in particular doesn't really imply anything.
>They can't. I don't know if there are quantum complications at that scale that change this picture, but my basic idea from classical physics is that Newton's Third Law says the probe can't have a force exerted on it by the sample (action) without also simultaneously itself exerting a force on the sample (reaction).
Well, that goes without saying. The question is if that "force" used to measure had any, well, measurable impact.
> > how they "feel" the interactions without disturbing them
> They can't. I don't know if there are quantum complications at that scale that change this picture, but my basic idea from classical physics is that Newton's Third Law says the probe can't have a force exerted on it by the sample (action) without also simultaneously itself exerting a force on the sample (reaction).
Best part about that line of reasoning is that it leads directly to the Heisenberg uncertainty principle which is definitely in play here. The act of them measuring the position of each of the atoms means that they can't know that the atoms aren't moving because of the force they exerted. On such small molecules they can likely be reasonably certain they haven't introduced any errors, but for a much larger sample they'll start to have issues where the act of measuring is going to change the outcome.
What I'm waiting for is when someone figures out how to make diffraction gratings for things in the 5nm area so that you can actually image this stuff with photons rather than with an AFM, that should let them handle larger sheets of graphene, and possibly even look at doped graphene with semiconductor properties to get a really awesome understanding of how and why it works (or doesn't).
I think what you're describing is the observer effect[1], not Heisenberg uncertainty[2].
Heisenberg uncertainty is much stronger than not being able to observe a system without disturbing it. It's more like, at a physical level, making the probability distribution of a position tight makes the distribution of momentum wide.
Well, there are a lot of quantum complications in this scale, the structure of the bounds is totally a quantum effect. And there are some problems with the Newton's Third Law when you consider the electromagnetic field. Anyway the general idea of force-reaction still holds, so it's a good approximation for this experiment. If the tip "see" the molecule, then the molecule "see" the tip.
The problem with your explanation is that the probe is much much bigger than 1 atom. It's a whole macroscopic tip, with a mass of a few grams. The tip of the tip use a single CO molecule, so the prove ends in a single atom, but the atom is attached to a big structure. If the tip were thicker, they would measure an average of the surface under the tip, with a very sharp tip they measure a small area.
The molecules are attached to a silver surface, so they are relatively fixed. The O atom in the CO molecule in the tip is approached to measure the force at each point of the surface. I couldn't find the exact distance but Wikipedia says that in similar experiments the distance is between 10A and 100A. For comparison, a bound between two Carbons in a molecule is approximately 1.5A. So the CO molecule is far away and the force is very small (in the absolute and the relative sense), and the system must use an incredible amount of amplification.
But the force in the sample molecule is also relatively small, so it isn't disturbed too much, and the data that you get are very similar to the data of the unperturbed molecule.
I suppose that it's possible to tweak the setting to decrease the distance so the interaction between the molecule in the tip and the sample molecule is smaller. I suppose that it's possible to use this to make some reactions happen, but I don't remember an experiment with this phenomenon. Anyway a usual problem is to crash the tip against the surface. It's bad for the tip, you need to pick another CO molecule and if it hit the sample molecule it could be interesting. With a similar microscope that use the tunnel effect it's possible to move atoms from one place to another, so it's possible to do things on the surface using the correct settings. You can even do a movie! https://news.ycombinator.com/item?id=5637150
I guess I didn't clearly state an additional assumption of my explanation. I assumed the oxygen atom has an electric charge, the rest of the probe structure is electrically neutral, and the electrostatic attraction/repulsion of charges is the mechanism by which the oxygen atom on the probe reacts to the sample [1].
So while the rest of the probe structure does exist, it's effectively [2] electrically neutral.
[1] I think we can agree that the gravitational attraction of the probe and sample to each other is way too small to matter.
[2] I think the large probe structure is close enough to neutral and/or far enough away from the sample to have an effect which is smaller than the effect of the oxygen atom. The structure may contribute some nontrivial amount of noise due to being neither exactly neutral nor infinitely far away, but not enough to totally drown out the signal from the oxygen atom.
I've found a previous article with more information and the full article available: "The chemical structure of a molecule resolved by atomic force microscopy" http://www.sciencemag.org/content/325/5944/1110
In this article, they explain that to get a good image, the distance between the tip and the molecule should be only ~1A. It's similar to the distance between atoms in the molecule, so the force is (relatively) big. Another important point is that using simulations to fit the data, they found that the main contribution to the force is not electrostatic, it's the Pauli repulsion (that is a quantum effect). Nevertheless if the tip "see" the molecule, then the molecule "see" the tip.
An important detail is that the Oxygen atom is small and it's not possible to measure how it is moved by the forces. The molecule applies a small force to the Oxygen atom that is attached to the Carbon atom that is attached to the big tip. The tip resonates like a tuning fork, and the small force on the Oxygen atom changes slightly the resonating frequency of the whole system. They measure this frequency shift and use it to calculate the force on the Oxygen atom.
Since the molecule is only heated momentarily to induce the reaction, it is cold before and after. The molecule might be effectively "stuck" to the silver surface it's resting on.
The molecules they were touching were perfectly flat, and must have been pretty well adhered to the silver surface. Now that I think about it, silver is used as a catalyst, and they had to heat it to 90C to cause the reaction. So it sounds like it was more of a problem of overcoming the inherent stability of the molecule to get it to do anything at all.
Well, as far as I understand it, the interactions (joints) manifest themselves as a larger density of electrons. That's pretty trivial (heh) to detect, just measure electrostatic interaction with a needle, or do some deflection fun.
When I looked at chemical symbols before seeing this I had always assumed them to be a sort of vague outline of what was really happening. It's amazing to think that the way chemicals bond is the same in reality as drawn in textbooks.
In the two variants on the right, their edges seem to be curling upward making a bowl shape. Their edges are also brighter, which perhaps means they are closer to the probe than parts that are farther away. Additionally, the hexagons are also not all the same shape. I assume that's due to the curling.
I would be interested to know if my interpretation of the image is correct, or if the molecule is really flat and what I'm seeing is an artifact.
To answer your question (flat vs. artifact) directly: It's flat. Sorta. Bear with me a moment. If this is confusing, please let me know, and i'll try to clarify. Molecular symmetry isn't my strong point, unfortunately.
The trouble with all of this is the "picture" is not an actual picture-made-with-photons picture, but a visualization via computer. That isn't to say it's a poor reflection on reality, but that the limitations of the techniques should be accounted for. In this case, the electron density of the overall molecule is being measured. The brighter signals correspond to an increase in local electron density.
In such chemical structures as these, the aromaticity [1] is the main force at play. Without getting too technical, the brighter regions are those with increased electron density. (See figure 4 at the IBM Zurich page on pentacene [2])
The hexagons (and square and pentagons) in fact do not have idealized geometry, but not due to any curling. The unique environment of each carbon is more at play. Symmetry plays a large role; imagine a symmetric vs. unsymmetrical tug-of-war between the carbons with the electrons as the rope. The left hand side and lower right have a dihedral mirror plane, simplifying the density somewhat, where the upper right has a more muddled situation.
Getting back to the flatness, the target molecule is 'mounted' on a suitably uniform surface, such that only one side is being scanned/read by the probe. In a vacuum, the tug of war in the Z direction (into the plane) will cancel out between the +Z and -Z vectors, giving a 'flat' molecule. (Depending on your point of view, either because of this or due to this, each of these molecules has a mirror plane in the plane of the molecule, bisecting each atom.)
Setting all that aside, the entire process is really #$%*& cool, particularly to a chemist. (Yes, those crazy textbook pictures are often reflected in reality. If only the different atoms were color coded, though!)
True. Even having a decent grasp on the topic (or perhaps, because having a decent grasp), I find it difficult to try to peel apart bond energy, electron density, bond length, etc, from each other; They're all effectively functions of each other and the entire system.
It sounds like you might be more up on this stuff than I am. Since the probe measures force, I was picturing it sort of pushing on the bond and registering the resistance, i.e. the bond energy. But that was just an impression, and I'm certainly no authority on this.
You don't really need much math to see why this is happening. First, the bonds in a benzene ring aren't discrete like we draw them, alternating between single bonds and double bonds. It's also important to realize that although we typically represent benzene in 2D all molecules really have a 3D geometry.
Electron orbitals can overlap in different ways depending on the geometry of the atom and its electronics. See this for a picture: http://en.wikipedia.org/wiki/File:Benzene_Representations.sv...
So, the electrons in a benzene ring really form more of a cloud around the entire ring. You'd expect this to pull the atoms into a perfect circle with the carbon atoms all being equidistance from each other, all else being equal.
However, each carbon atom also has a hydrogen atom attached to it. So now you have a sort of a circle with 6 "strings" attached at points equidistant around the circle all pulling outward, perpendicular to the circle.
Imagine a perfectly circular piece of string with 6 strings attached equidistantly around the circle. You apply an equal force perpendicular to the surface of the circle.
Hopefully you can see how this would result in the original circular string being "deformed" into a hexagon.
It's a far leap from there to say why hexagons are "so common in nature." Are they? Relative to what? I don't know that any of this has anything to do with the shape of that storm you linked to.
> It's a far leap from there to say why hexagons are "so common in nature."
I was thinking of things (compared to other geometric shapes) like the storm, honey bee cells (honeycombs), basalt columns [1], turtle shells (although irregular), and a common snowflake shape.
There are three regular polygons you can use to tile a plane: triangles, squares, and hexagons. The regular hexagonal packing is the densest sphere packing in the plane, so any time you have objects constrained to a plane which for the sake of maximizing or minimizing some force want to be equidistant from each other you'll get something close to a hexagon.
I'll add that sometimes a shape like that might result from a more evolutionary process. In a 2D plane a circle is the structure which most equally distributes force, so it's the shape most able to hold up under pressure.
But a tile of circles isn't so fortunate. Of all the possible tilings, the hexagonal tiling holds up the best precisely because it's the densest sphere packing in the plane.
Other arrangements might appear, but over the course of time you're more likely to see hexagonal tilings since those are the ones that best survive external forces.
It has to do with the bond angles in water molecules. The bond angles are, in turn, determined by quantum mechanical wave functions. These quantum mechanical wave functions apply to all of chemistry, including benzene rings. So the shapes of snowflakes and the shapes of benzene rings are not totally independent events.
The short answer for why benzene rings are common is aromaticity, which makes it a very stable structure. Rings with fewer than 6 members are uncommon in chemistry, because the angles are not what the bonds naturally want to be and so they are increasingly unstable.
As for nature in general, you could probably come up with a convincing argument that boils down to: 6 is a nice round number. It has 2 and 3 as factors.
>Rings with fewer than 6 members are uncommon in chemistry
In chemistry, or in nature? five membered rings show up all over the place, both aromatic and otherwise. Granted, cyclobutyl (4 member, square) and cyclopropyl (3 membered, triangle) suffer from ring strain and are uncommon, but 5, 6, 7, (or higher) rings show up all over the place.
Examples off the top of my head are the cyclopentadienyl ion pervasive in inorganic chemistry (see ferrocene, et al) and amino acids tryptophan, tyrosine, histidine, and phynylalanine all feature cyclic aromatics 5 and 6 membered, as well as proline with a non-aromatic 5 member ring.
The takeaway point is that although ring-strain (having non ideal angles (120 or 109.5 degrees)) increases the internal energy of the molecule (destabilizing it), other factors, such as aromaticity, which decrease internal energy (stabilizing it) may balance or exceed the ring-strain, still giving a stabilized, if non-ideal geometry.
(But yeah, 3, 4 membered rings, ugh. Look up platonic alkanes for some really crazy strain angles.)
Not sure how they "feel" the interactions without disturbing them but that's why they are the physicists.