A chain reaction with no return
Keith S. Taber
Have chemist's created an atomic scale Newton's cradle?
(Image by Michelle from Pixabay)
Mimicking a Newton's cradle
I was interested to read in an issue of Chemistry World that
"Scientists in Canada have succeeded in setting off a chain of reactions in which fluorine atoms are passed between molecules tethered to a copper surface. The sequence can be repeated in alternating directions, mimicking the to-and-fro motions of a Newton's cradle."
Blow, 2022
The Chemistry World report explained that
"The team of researchers…affixed fluorocarbons to a [copper] surface by chemisorption, constructing chains of CF3 molecules terminated by a CF2 molecule – up to four molecules in total….
The researchers applied an electron impulse to the foremost CF3 molecule, causing it to spit out a fluorine atom along the chain. The second CF3 absorbed this atom, but finding itself unstable, ejected its leading fluorine towards the third molecule. This in turn passed on a fluorine of its own, which was taken up by the taken up by the CF2 molecule in fourth position."
Blow, 2022
There is some interesting language here – a molecule "spits out" (a metaphor?) an atom, and another "finds itself" (a hint of anthropomorphism?) unstable.
Can a line of molecules 'tethered' onto a metal surface behave like a Newton's cradle?
Generating reverse swing
The figure below was drawn to represent the work as described, showing that "another electron impulse could be used to set… off…a reverse swing".
That reference to "another electron impulse" being needed is significant,
"What was more, each CF3 had been flipped in the process, so the Newton's cradle as a whole was a mirror image of how it had begun, giving the potential for a reverse swing. Unlike a desk Newton's cradle, it did not swing back on its own accord, but another electron impulse could be used to set it off."
Blow, 2022
Mirroring a Newton's cradle
Chemistry World is the monthly magazine of the Royal Society of Chemistry (a learned society and professional body for chemists, primarily active in the UK and Eire) sent to all its members. So, Chemistry World is part of the so-called secondary literature that reports, summarises, and comments on the research reports published in the journals that are considered to comprise the primary academic literature. The primary literature is written by the researchers involved in the individual studies reported. Secondary literature is often written by specialist journalists or textbook authors.
The original report of the work (Leung, Timm & Polanyi, 2021) was published in the research journal Chemical Communications. That paper describes how:
"Hot [sic] F-atoms travelling along the line in six successive 'to-and-fro' cycles paralleled the rocking of a macroscopic Newton's cradle."
Leung, Timm & Polanyi, 2021, p.12647
These authors explain that
"…energised F can move to- and-fro. This occurs in six successive linear excursions, under the influence of electron-induced molecular dissociation at alternate ends of the line…. The result is a rocking motion of atomic F which mirrors, at the molecular scale, the classic to-and-fro rocking of a macroscopic Newton's cradle. Whereas a classic Newton's cradle is excited only once, the molecular analogue [4] here is subjected to opposing impulses at successive 'rocks' of the cradle.
The observed multiple knock-on of F-atoms travelling to-and-fro along a 1D row of adsorbates [molecules bound to a substrate] is shown…to be comparable with the synchronous motion of a Newton's cradle."
Leung, Timm & Polanyi, 2021, p.12647-50
Making molecules rock?
'Rocking' refers to a particular kind of motion. In a macroscopic context, there are familiar example of rocking as when a baby is cradled in the arms and gently 'rocked' back and forth.
A rocking chair is designed to enable a rocking motion where the person in the chair moves back and forth through space.
The molecular system described by Leung and colleagues is described as "mirror[ing], at the molecular scale…to-and-fro rocking"
[Image by OpenClipart-Vectors from Pixabay]
The researchers are suggesting that, in some sense, the changes in their molecular scale system are equivalent to "the synchronous motion of a Newton's cradle".
Titles and texts in scientific writing
One feature of interest here is a difference between the way work is described in the article titles and the main texts.
| Chemistry society professional journal | Academic research journal | |
| Title | "…molecular Newton's cradle" | "…an atomic-scale Newton's cradle" |
| Text | The effect was "mimicking … a Newton's cradle." | The effect "paralleled… mirrors… [is] comparable with" Newton's cradle |
Titles need to capture the reader's attention (and in science today the amount of published material is vastly more than only one person could read) so there is a tendency to be bold. Both these articles have titles suggesting that they are reporting a nanoscopic Newton's cradle. The reader enticed to explore further then discovers that there are caveats. What is being claimed is not a Newton's cradle at minuscule scale but something which though not actually a Newton's cradle, does have some similarity to (mimics, parallels, mirrors) one.
This is important as "the molecular analogue" is only analogous in some respects.
The analogy
There is an analogy, but the analogy can only be drawn so far. In the analogy, the suspended balls of the Newton's cradle are seen as analogous to the 'chemisorbed' molecules lined up on the surface of a copper base.
Analogies are used in teaching and in science communication to help 'make the unfamiliar familiar', to show someone that something they do not (yet) know about is actually, in some sense at least, a bit like something they are already familiar with. In an analogy, there is a mapping between some aspect(s) of the structure of the target ideas and the structure of the familiar phenomenon or idea being offered as an analogue. Such teaching analogies can be useful to the extent that someone is indeed highly familiar with the 'analogue' (and more so than with the target knowledge being communicated); that there is a helpful mapping across between the analogue and the target; and that comparison is clearly explained (making clear which features of the analogue are relevant, and how).
Analogies only map some features from analogue to target. If there was a perfect transfer from one system to the other, then this would not be an analogy at all, but an identity! So, in a sense there are no perfect analogies as that would be an oxymoron. Understanding an analogy as intended therefore means appreciating which features of the analogue do map across to the target, and which do not. Therefore in using analogies in teaching (or communicating science) it is important to be explicit about which features of the analogue map across (the 'positive' analogy) and which do not, including features which it would be misleading to seek to map across – the so called 'negative analogy.' For example, when students think of an atom as a tiny solar system, they may assume that atom, like the solar system, is held together by gravitational force (Taber, 2013).
It probably seems obvious to most science teachers that, if comparing the atom with a solar system, the role that gravity has in binding the solar system maps across to the electrical attraction between a positive nucleus and negative electrons; but when a sample of 14-18 year-olds were asked about atoms and solar systems, a greater number of them suggested the force binding the atom was gravitational than suggested it was electrical (Taber, 2013)!
Perhaps the most significant 'negative analogy' in the research discussed here was pointed out in both the research paper and the subsequent Chemistry World report, and relates to the lack of inherent oscillation in the molecular level system. The nanoscopic system is like a Newton's cradle that only has one swing, so the owner has to reset it each half cycle.
- "Unlike a desk Newton's cradle, it did not swing back on its own accord, but another electron impulse could be used to set it off."
- "Whereas a classic Newton's cradle is excited only once, the molecular analogue here is subjected to opposing impulses at successive 'rocks' of the cradle"
That is quite a major difference when using the Newton's cradle for an analogy.
Who wants a Newton's cradle as an executive toy if it needs to be manually reset after each swing?
The positive and negative analogies
We can consider that the Newton's cradle is a little like a simple pendulum that swings back and forth, with the complication that instead of a single bob swinging back and forth, the two terminal spheres share the motion between them due to the momentum acquired by one terminal sphere being transferred thorough the intermediate spheres to the other terminal sphere.
In understanding the analogy it is useful to separately consider these two features of a Newton's cradle
- a) the transfer of momentum through the sequence
- b) moving a mass through a gravitational field
If we then think of the Newton's cradle as a 'pendulum with complications' it seems that the molecular system described by Leung and colleagues fails to share a critical feature of a pendulum.
A chain reaction – the positive analogy
The two systems map well in so far as that they comprise a series of similar units (spheres, molecules) that are carefully aligned, and constrained from moving out of alignment, and that there is a mechanism that allows a kind of chain reaction.
In the molecular scenario, the excitation of a terminal molecule causes a fluorine atom to become unbound from the molecule and to carry enough momentum to collide with and excite a second molecule, binding to it, whilst causing the release of one of the molecule's original fluorine atoms which is similarly ejected with sufficient momentum to collide with the next molecule…
This 'chain reaction' 5 is somewhat similar to how, in a Newton's cradle, the momentum of a swinging sphere is transferred to the next, and then to the next, and then the next, until finally all the momentum is transferred to the terminal sphere. (This is an idealised cradle, in any real cradle the transfer will not be 100% perfect.) This happens because the spheres are made from materials which collide 'elastically'.6
The negative analogy
Given that positive mapping, a key difference here is the way the components of the system (suspended spheres or chemisorbed molecules) are 'tethered'.
Chemisorbed molecules
The molecules are attached to the copper surface by chemical bonding, which is essentially an electromagnetic interaction. A sufficient input of energy could certainly break these bonds, but the the impulse being applied parallel to the metal surface is not sufficient to release the molecules from the substrate. It is enough to eject a fluorine atom from a molecule where carbon is already bound to the surface and three other fluorines atoms (carbon is tetravalent, but it is is bonded to the copper as well as the fluorines) – but the final molecule is an adsorbed CF2 molecule, which 'captures' the fluorine and becomes an absorbed CF3 molecule.
Now, energy is always conserved in all interactions, and momentum is also always conserved. If the kinetic energy of the 'captured' fluorine atom does not lead to bond breaking it must end up somewhere else. The momentum from the 'captured' atom must also be transferred somewhere.
Here, it may be useful to think of chemical bonds as having a similarity to springs – in the limited sense that they can be set vibrating. If we imagine a large structure made up of spheres connected by springs, we can see that if we apply a force to one of the spheres, and the force is not enough to break the spring, the sphere will start to oscillate, and move any spheres connected to it (which will move spheres attached to them…). We can imagine the energy from the initial impulse, and transferred through the chain of molecules, is dissipated though the copper lattice, and adds to its internal energy. 7
Working against gravity
In a simple pendulum, work is done on a raised sphere by the gravitational field, which accelerates the bob when it is released, so that it is moving at maximum speed when it reaches the lowest point. So, as it is moving, it has momentum, and its inertia means it continues to swing past the equilibrium position which is the 'attractor' for the system. In a Newton's cradle the swinging sphere cannot continue when it collides with the next sphere, but as its momentum is transferred through the train of spheres the other terminal sphere swings off, vicariously continuing the motion.
In an ideal pendulum with no energy losses the bob rises to its original altitude (but on the other side of the support) by which time it has no momentum left (as gravitational force has acted downwards on it to reduce its momentum) – but gravitational potential energy has again built up in the system to its original level. So, the bob falls under gravity again, but, being constrained by the wire, does not fall vertically, rather it swings back along the same arc.
It again passes the equilibrium position and returns to the point where it started, and the process is repeated. In an ideal pendulum this periodic oscillation would continue for ever. In a real pendulum there are energy losses, but even so, a suitable bob can swing back an forth for some time, as the amplitude slowly reduces and the bob will eventually stop at the attractor, when the bob is vertical.
In a (real) Newton's cradle, one ball is raised, so increasing the gravitational potential energy of the system (which is the configuration of the cradle, with its spheres, plus the earth). When it is released, gravity acts to cause the ball to fall. It cannot fall vertically as it is tethered by a steel (or similar) wire which is barely extendible, so the net force acting causes the ball to swing though an arc, colliding with the next ball.
(Image by 3D Animation Production Company from Pixabay)
Two types of force interactions
The steel spheres, however, are actually subject to two different kinds of force. They are, like the molecules, also tethered by the electromagnetic force (they are attached to steel wires which are effectively of fixed length due to the bonding in the metal 8), but, in addition, subject to the gravitational field of the earth. 9 The gravitational field is relevant because a sphere is supported by a wire that is fixed to a rigid support (the cradle) at one end, but free to swing at the end attached to the sphere.
The Newton's cradle operates in what is in effect a uniform gravitational field (neither the radial nature or variation with altitude of the earth's field are relevant on the scale of the cradle) – and the field direction is parallel to the plane in which the balls hang. So, the gravitational potential of the system changes as a sphere swings higher in the field.
The design of the system is such that a horizontal impulse on a sphere leads to it swinging upwards – and gravity then acts to accelerate it towards a new collision. 10 This collision, indirectly, gives a horizontal impulse to the sphere at the other end of the 'train' where again the nature of the support means the sphere swings upward – being constrained by both the wire maintaining its distance from the point of suspension at the rigid support of the frame, and its weight acting downwards.
The negative analogy concerns the means of constraining the system components
The two systems then both have a horizontal impulse being transferred successively along a 'train' of units. Leung and colleagues' achievement of this at the molecular scale is impressive.
However, the means of 'tethering' in the two systems is different in two significant ways. The spheres in the Newton's cradle are suspended from a rigid frame by inextensible wires that are free to swing. Moreover, the cradle is positioned in a field with a field direction perpendicular to the direction of the impulse. This combination allows horizontal motion to be converted to vertical motion reversibly.
The molecular system comprises molecules bound to a metal substrate. The chemisorbtion is less like attaching the molecules with long wires that are free to swing, and more like attaching them with short, stiff springs. Moreover, at the scale of the system, the substrate is less like a rigid frame, and more like a highly sprung mattress. So, even though kinetic energy from the 'captured' fluorine atom can be transferred to the bond, this can then be dissipated thorough the lattice.
The molecular system does not enable the terminal molecule to do work in some form that can be recovered to reverse the initial process. By contrast, a key feature of a Newton's cradle is that the spheres are constrained ('tethered') in a way that allows them to move against the gravitational field – they cannot move further away from, nor nearer to, their point of support, yet they can swing up and down and change their distance from the earth. Mimicking that kind of set-up in a molecular level system would indeed be an impressive piece of nano-engineering!
Work cited:
- Blow, M. (2022). Molecular Newton's cradle challenges theory of transition states. Chemistry World, 19(1), 38.
- Leung, L., Timm, M. J., & Polanyi, J. C. (2021). Reversible 1D chain-reaction gives rise to an atomic-scale Newton's cradle. Chemical Communications, 57(94), 12647-12650. doi:10.1039/D1CC05378G
- Taber, K. S. (2013). Upper Secondary Students' Understanding of the Basic Physical Interactions in Analogous Atomic and Solar Systems. Research in Science Education, 43(4), 1377-1406. doi:10.1007/s11165-012-9312-3 (The author's manuscript version may be downloaded here.)
Notes
1 Strictly they are no distinct atoms once several atoms have been bound together into a molecule, but chemists tend to talk in a shorthand as if the atoms still existed in the molecules.
2 Whilst I expect this is obvious to people who might choose to read this posting, I think it is worth always being explicit about such matters as students may develop alternative conception at odds with scientific accounts.
In the present case, I would be wary of a learner thinking along the lines "of course the atom will go back to its own molecule"
Students will commonly transfer the concepts of 'ownership' and 'belonging' from human social affairs to the molecular level models used in science. Students often give inappropriate status to the history of molecular processes (as if species like electrons recall and care about their pasts). One example was a student who suggested to me that in homolytic bond breaking each atom would get its own electron back – meaning the electrons in the covalent bond would return to their 'own' atoms.
I have also been told that in double decomposition (precipitation) reactions the 'extra' electron in an anion would go back to its own cation in the reagents, before the precipitation process can occur (that is, precipitation was not due to the mutual attraction between ions known to be present in the reaction mixture: they first had to become neutral atoms that could then from an ionic bond by electron transfer!) In ionic bonding it is common for learners to think that an ionic bond can only be formed between ions that have been formed by a (usually fictitious) electron transfer event.
Read about common alternative conceptions of ionic bonding
3 I have here represented the same molecules both as atoms linked by bonds (where I am focusing on the transfer of fluorine atoms) and in other diagrams as unitary spheres (where I am focusing on the transfer of energy/momentum). All models and representations used for atoms and molecules are limited and only able to reflect some features of what is being described.
4 A note on terminology. An analogy is used to make the unfamiliar familiar by offering a comparison with something assumed to already be familiar to an audience, in this case the molecular system is the intended target, and the (that is, a generic) Newton's cradle is the analogue. However, analogy – as a mapping between systems – is symmetrical so each system can be considered the analogue of the other.
5 In some way's Leung's system is more like a free radical reaction than a Newton's cradle. A free radical is an atom (or molecule) with an unpaired electron – such as an unbound fluorine atom!
In a free radical reaction a free radical binds to a molecule and in doing so causes another atom to be ejected from the molecule – as a free radical. That free radical can bind to another molecule, again causing it to generate a new free radical. In principle this process can continue indefinitely, although the free radical could also collide with another free radical instead of a molecule, which terminates the chain reaction.
6 The balls need to be (near enough) perfectly elastic for this to work so the total amount of kinetic energy remains constant. Momentum (mv) is always conserved in any collision between balls (or other objects).
If there were two balls, then the first (swinging) sphere would be brought to a stop by the second (stationary) sphere, to which its momentum would be transferred. So, the first ball would stop swinging, but the second would swing in its place. The only way mv and mv2 (and so kinetic energy) can be both conserved in collisions between balls of the same mass is if the combination of velocities does not change. That is, mathematically, the only solutions are where neither of the two balls' velocities change, or where they are swapped to the other permutation (here, the velocity of the moving ball becomes zero, but the stationary ball moves off with the velocity that the ball that hit it had approached it with).
The first solution would require the swinging steel ball to pass straight through the stationary steel ball without disturbing it. Presumably, quantum mechanics would suggest that ('tunnelling') option has a non-zero (but tiny, tiny – I mean really tiny) probability. To date, in all known observations of Newton's cradles no one has reported seeing the swinging ball tunnel though the stationary ball. If you are hoping to observe that, then, as they say, please do not hold your breath!
With more balls momentum is transferred through the series: only the final ball is free to move off.
7 We can imagine that in an ideal system of a lattice of perfectly rigid spheres attached to perfect springs (i.e., with no hysteresis) and isolated from any other material (n.b., in Leung et al 's apparatus the copper would not have been isolated from other materials), the whole lattice might continue to oscillate indefinitely. In reality the orderliness will decay and the energy will have in effect warmed the metal.
8 Strictly, the wires will be longest when the spheres are directly beneath the points of support, as the weight of a sphere slightly extends the wire from its equilibrium length, and it will get slightly shorter the further the sphere swings away from the vertical position. In the vertical position, all the weight is balanced by a tension in the wire. As the ball swings away from the vertical position, the tension in the wire decreases (as only the component of weight acting along the wire needs to be balanced) and an increasing component of the weight acts to decelerate it. But the change in extension of the wire is not significant and is not noticeable to someone watching a Newton's cradle.
When the wire support is not vertical a component of the weight of the sphere acts to change the motion of the sphere
9 Molecules are also subject to gravity, but in condensed matter the effect is negligible compared with the very much stronger electromagnetic forces acting.
10 We might say that gravity decelerates the sphere as is swings upwards and then accelerates as it swings back down. This is true because that description includes a change of reference direction. A scientist might prefer to say that gravity applies a (virtually) constant downward acceleration during the swing. This point is worth making in teaching as a very common alternative conception is to see gravity only really taking effect at the top of the swing.
