So in the second part of lecture, 13 will begin by having a look at some molecules that have been designed specifically to have as lower beta value as possible.

Until then, we'll have a look at what happens as a consequence of that.

And we'll consider what happens when the molecules get longer than about four nanometers.

So we saw before.

Not for simple.

Find me sound contacted A Liga thiophenes the beta value is quite quite high.

But this isn't necessarily always the case for illegal things.

Some Japanese workers made these molecules here, which are designed to have.

Extremely low beta values. Extremely high conjugation, So what they did?

Was there made these staffing monomers with this Spyro SP3 carbon? Here grafted to a florene unit that's got terminal secondary alkyl groups to solubilize the molecules. Now because of this SP3 carbon here.

Although I've written this, it's easy to show the structure in this particular way in two dimensions. Of course, this flooring group is actually orthogonal to the seifein ring.

The consequence of that is that if you make a ligaments of these.

The very bulky florene spiral flooring group, here's.

Rigidly enforces the thiophenes to be coplanar.

So that these groups can stay out of each other's way as much as possible.

So the fifing rings alternating orientation, up, down, up, down.

And and effectively, more or less completely coplanar.

And on not flexible.

So this makes them the Malta conjugation much higher than an ordinary illegal thing that doesn't have these groups.

And so these workers made a whole range of molecules. In fact, up to 24 fifing rings. Very impressive. Bit of synthetic chemistry.

And they measured the conductance using STM break junction technique.

And they found that four shorter, the shorter leg of Thiophenes.

They conducted by tunneling.

The log of conductance fell linearly with increasing length and the beta value was only two per nanometer.

Now these molecules, all this work was done using these terminal icefire cyanide groups and when these form junctions, as I said before, the carbon sulfur bonds are pretty certainly break, and so these molecules probably are contacting the gold through thiolate rather than through thio ethers.

So it may be actually the nature of the contact. Chemistry can also affect this beta value.

So another system that was designed specifically to have as lower beta value as possible.

Involved these porphyrin molecules.

And again, Becausw very conjugated oligomer's are likely to be rather insoluble in organic solvents, making handling these molecules for conductance measurements quite difficult.

The porphyrin ring also has these substituents here, with these long alkoxy chains.

Which are designed to help keep the molecule in solution.

And Becausw again, although I've written this as if it's playing and it's not because of the.

Because of starrick interactions between these author hydrogens, here these two benzene rings are twisted out of conjugation with the porphyrin, and so this means that these alkoxy substituents spend most of their time above and below the conjugation plane of the illegal porphyrin and that prevents intermolecular interactions as well.

So again, the contact chemistry here is thiolate.

And a small range of molecules or ligaments was made with 1, two and three porphyrin rings, and they're separated by butadiene connectors.

So there are two carbon carbon triple bond units between each porphyrin.

And as part of this study as well, the sort of.

Parent molecules made weather and otpor friends between the between the contact groups.

And this is a plot of the log of the conductance against the sulfur sulfur separation in the molecules.

And so these molecules conduct again by a tunneling mechanism.

And the beta value is very small. It's only about .4 per nanometer.

Similarly, if you look at a series of legal lines.

So that's without any porphyrins in, just carbon, carbon, triple bonds, varying lengths.

These turn out also to have a very low beta value.

Species of this sort, known to exist in interstellar space.

So it's quite interesting that there are potentially very good molecular wires in interstellar space.

So the beta value for this system is about .6 per nanometer.

In this case, it was necessary to use pyridine as the contact groups.

Because parading is relatively electron withdrawing, and that helps to stabilize the longer illegal car bines becausw as you make these molecules longer, they tend to get unstable.

So if if we can lower beta values to that extent.

The question then arose if you if you make the **** LUMO separation in longer oligomer is really small.

Can you actually get to a situation where either the **** or the LUMO?

Coincides with the Fermi energy of the metal Contacts.

If you could do that, then you would get what's called resonant tunneling. In other words, the transmission through the molecule would be unity.

The TAV will be one, and so the conductance through the molecule would be G nought.

It'll be as conductive as a chain of metal atoms.

And one piece of work along these lines was done by groups in the US, and they used the donor acceptor principle, which we've already met in organic photovoltaics and thin film transistors in in polymers.

And so they made a series of molecules with one, 2, three and four repeat units. Here, with in this case Fioe file contact groups on the ends, and again these secondary alkyl groups both to solubilize these one conjugated molecules and to stop or at least limit intermolecular interactions.

Only use the STM break junction technique. We're going to measure the conductance.

This is a UV visible Spectra of these oligomer's with one, 2, three and four.

Repeat units here.

And by the time you're at three or four units, the this peak is moving into the red part of the visible spectrum are really conjugated, so the pipeline star transition occurs at really low energy even for relatively shorter ligaments.

And if you measure the conductance of these molecules as a function of length using a very small bias voltage of only .09 volts.

Then you can see that in the in the histogram.

From the from the peaks. Here for the molecule with 1, two and three.

Repeat units, does it clearly, a decrease in the in the conductance or in the log of the conductance as a function of length?

And it's behaving like a normal tunneling system.

And if you workout the beta value for that, it's about 1.8 per nanometer.

So again, because we've got a low home or luma separation, we've got a low beta value.

But the interesting thing is that if you increase the bias voltage to quite a high value, actually about .65 volts.

You see something completely different.

You see that.

If you go initially from one molecule to 21, repeat unit to two, the conductance peak actually increases.

And then once you've gone to two, if you go to three or four repeat units.

Essentially, the the position of this peak doesn't really shift very much at all.

So the conductance increases from N = 1 to N = 2 and then it stays there.

And.

You could object to this by saying, well, you're using a high bias voltage here.

And so maybe what's happening is that when you lift the molecule up from the surface, 'cause it'll probably live more or less flat on the gold until that it picks the molecule up.

Maybe what's happening is that the conductance that the junction breaks down before you fully lifted the molecule into the.

Into the gap, and so the conduction is actually from the tip through the Pi conjugated system in the molecule and then into the other gold electrode without it actually going along the whole backbone of the molecule.

But that objection doesn't seem to apply because if you take the.

The trimmer

and you do one of these so called 2 dimensional conductance plots where you measure you plot out all of the conductance plateaus.

Some together.

And you express the frequency of occurrence in a current in a color density plot.

You find that the plateau is actually the average plateau.

Extends out to about 2 1/2 or three nanometers, and that corresponds to the length of the full length of the tryma molecule.

So they are being lifted up properly into the gap.

So what's the explanation for this? Why? Why does the conduction not really change as a function of length for these molecules?

Well, this is where some theoretical calculations come in. Useful. We saw already the Landauer formula.

G cost G nought times the transmission.

And where TV is the transmission function value at the Fermi energy of the Contacts.

And the calculation showed that.

The conductance is indeed predicted to fall exponentially with length if the bias voltage is low, so these are the transmission functions for the different length molecules. The Red line is for one.

The green line to the Blue Line 3 and the yellow line for repeat units.

And so for the.

For the shortest molecule.

Within this energy range here.

We only see two resonances, that's the.

That's the LUMO resonance and that's the **** resonance.

And then those are sort of well in the middle.

And this is typical for thio Ether Contacts that the Fermi energy tends to form somewhere in the middle of this well. And in fact it's neat. It's slightly nearer to the **** resonance than to the LUMO resonance.

So to calculate the conductance we read off the transmission. Here the calculated transmission.

At the Fermi energy. So that's zero here.

And we see it should be about 10 to the minus 2G nought.

And then if we make the molecules longer, the conductance falls.

Now these plots are always.

What you get out of these plots is always the system at zero bias.

So approximately the conductance will correspond to the conductance at less than .1 volts will probably fall somewhere in this range. We can be fairly sure of that.

So the takehome message from this is that although the **** LUMO separation decreases with the length.

And you can see that from the fact that as you make the molecules longer, you get more and more resonances close together here.

The degree of molecule contact coupling also decreases, so you can see that the two resonances for the shortest molecule are really broad.

Alright, that indicates that there's a high degree of metal molecule coupling for the shortest molecule.

But when you go from N = 1 to N = 2, You can see that for the dimer the two resonance is here.

Alright, for the **** in the LUMO are quite a bit sharper and then they stay pretty sharp. In fact they get even sharper when you make the molecule longer and the sharpness of those residents that decrease metal molecule coupling.

Means that the well actually gets deeper, and that's probably why the molecules conductance decreases with length.

Now.

We can't really.

Easily extrapolate this plot to hide biases, but because the **** LUMO separation for the longer molecules is very small.

What will happen?

If we increase the biases that we what we're doing effectively is climbing up this curve, climbing up these curves here.

And because this is a low bang up system and this energy scale is quite small, the energy scale here is actually comparable with the bias voltage. So if we make the bias .65 volts, what we're doing is we're shift shuffling along this.

Along this axis, here to a point somewhere around, probably around here.

So as we climb up these curves, you can see that at this point here, all of these curves more or less intersect.

And so that's a handwaving explanation for why. If we apply a high bias.

The conductances of the molecules don't really change as a function of length.

Because the transmissions here all crossover.

So then would if we could actually shift them a bit further and get right to the point of the resonance here near minus .3 V, why the home OS?

Then the transmission would actually be one and then, and the molecule would conduct like a chain of metal atoms, and that's what's called resonant tunneling. Now we haven't. We obviously. At least people haven't quite achieved that.

Because the conductances of all the longer molecules were about 5 * 10 to the minus 3G nought. But that's still a really high value actually for these long molecules, one of the highest values that's been seen.

So.

You can see that by lowering the bank app deliberately to a very small manga system.

We can approach the point at which we were near resonant tunneling resonant conductance.

So so far I've just assumed I've just told you that the mechanism is is tunneling.

And we know that for these molecules, well, as we've seen, you can measure the conductance as a function of molecular length.

And the conductance length, relationship should be exponential.

But something else that you can also do is to examine the conductance as a function of temperature.

Turn in a tunneling mechanism.

Tunnelling is not a thermally activated process, so there should be no temperature dependence. The conductance of the system should not change as a function of temperature. If the mechanism is tunneling.

Answer For all the families and molecules I've mentioned so far.

Where experiments of this type of being done.

It's been shown that there isn't a temperature dependent, so they do conduct by by tunneling.

But the question arises what happens at longer lengths?

What happens if we make molecules longer?

Well, if you make molecules longer.

Because tunneling decays exponentially.

Then if there's a possibility for hopping.

Then the hopping mechanism can come in into play for longer molecules.

And there is a difference between tunneling and hopping.

Another feature of tunneling, which I haven't really mentioned so far, is that tunneling is what's called a coherent process.

So you wouldn't be able to to distinguish an electron. The tunnel through the molecule into one contact from any other electron within the contact.

The electron will keep all of its properties as its tunneled through the molecule.

But hopping is not a coherent process.

In hopping, what happens is that an electron will spend a finite length of time in a molecular orbital in the bridging molecule.

And so the molecule will then undergo a relaxation to accommodate the extra electron.

The surrounding solvent will change its position to accommodate the new dipole moment of the molecule or the new charge state of the molecule.

And so the electron then loses what's called its coherence. Once it gets through them. Once it gets off the molecule again and onto the other contact, it's lost. The properties that it had originally.

So because this business necessity for the molecule to relax, there is an activation energy for getting them the electron from the contact into into a molecular orbital or from a molecular orbital on the metal into the contact.

There is an activation energy and therefore the conductance in the tunneling mechanism will be temperature dependent.

Another consequence of it is the.

But it's it decays. The conductance decays with length in a linear relationship, not an exponential one. So conductance falls less deeply with increasing length of the molecule than it does in a tunneling relationship.

So this is an early case where hopping was suggested to come in for longer molecules.

So to get these molecules long enough, these workers had to use a new kind of strategy.

And what they did?

Once they built up their molecules on the flat gold surface.

Using this sort of repetitive chemistry, So what they did was they took this.

Amino fire fenal

and so at least a gold sofa lights gold so it selectively binds to goal through the sulfur, leaving you with a terminal aiming group.

And then once you've got the self assembled monolayer of the molecules close, packed on the gold.

You expose it to a solution of this this dialdehyde here.

And you get a condensation reaction. Formation of any mean bond.

And this is conjugated.

And now you've got a terminal aldehyde group.

So then you take another solution.

With benzene 14 diamine in it.

Do another condensation and now you've got a new imming bond with a terminal aiming group.

And we are with the more of the DI aldehyde and you can build up the oligomer.

To his long a length as you like, at least in principle.

And to be sure that they were actually achieving this, they measured romance Spectra of these.

Surface and they looked at the functional group interconversion in the in the romance spectrum, they said.

There's a distinctive peak for the way you've got terminal terminal aldehyde groups, so that appears then disappears when it's a diamine and then reappears when you've reacted with more aldehyde disappears when you're out with more diamine reappears when you react with more aldehyde, and so on.

So you can actually follow these reactions.

On one night made the molecules as long as they wanted.

They terminated the growing chain by reacting it with a mono aldehyde on mono way mean. So there's no functional group left at the end.

Now obviously they couldn't use the STM break junction for this because there's no contact group at the end here, and they actually used the conducting atomic force microscopy technique to measure the electrical properties of these junctions.

So what did they get?

Well, here we plot the log of the resistance, so they use resistance rather than conductance. But the two are just once the reciprocal of the other.

And you can see that as we make the ligaments longer.

The longer the resistance linearly increases with the length.

On the slope of that line there.

Is about 3 per nanometer.

Now when you get to about four nanometers, which is this oh P I5 here.

A pentima

you get a change in the slope of this plot.

And if you put another straight line through the later points here, the slope is smaller.

Beta is only now .9 per nanometer.

So.

Obviously some other mechanism is now taking over from tunneling as the predominant mechanism.

And that mechanism is probably hopping.

Now in hopping as I said, the conductance should fall linearly with length and not exponentially. And actually if you look at these points you can see that this isn't really a straight line. There's a distinct curvature there an so if this was plotted as just the resistance rather than the log of the resistance, it would probably be a straight line.

So this beta value is a bit nominal because it's not really a tunneling mechanism anyway.

So that's what led them to suspect that a hopping mechanism was coming in, and when they suspected that.

Ladies, I need to do some temperature dependent measurements.

So the change kicks in at 4 four nanometers length.

And.

What they found was that for monolayers of longer than four nanometers the conductance was also temperature dependent whereas for monomouse for ligaments of less than four nanometers. It was not temperature dependent so this is arenius type lots.

Reciprocal temperature against the resistance here.

How long of resistance?

And you can see that 40 P I4, so that's this one.

Which is on this curve.

Well, it's just the tunneling mechanism.

There's essentially no temperature dependence of the conductance.

Or resistance.

But for OP I6 and for OP I-10.

There is a distinct temperature dependence of the conductance.

And so that's all consistent with the hopping mechanism coming in.

For longer molecules.

Now I should point out that this paper isn't really a single molecule conductance paper.

Becausw

conducting AFM tips or are relatively shallow and they have quite a large area.

And so, in this experiment, you're sort of using pressure to press the tip down on the monolayer, and you probably conduct contacting somewhere between dozens and hundreds of molecules at a time.

But nonetheless, if you use a constant force to apply the tip to the surface, you're going to have roughly the same number of molecules each time in the junction. When you do these experiments.

So these results are probably fairly reliable.

So this is the first time that people had.

Seeing evidence for hopping mechanism in metal molecule metal junctions.

So in conclusion, for this conductance part of the course.

Um?

We asked the question what kind of structure should we make to carry charge well and can we make anything approaching a true molecular wire like chain of gold atoms?

And the answer is that clearly some structures do give better molecular wise than others with lower beta values.

And what you really need is a small home olumo gap.

And ideally a strong gold metal contact as well.

But even with that, even with a very low home olumo gap.

The absolute values of conductances are still quite low.

And much less than the quantum unit of conductance for chain of metals.

To the question, how do molecules carry charge and what's the metal of mechanism of conductance? While we've seen that tunneling is the dominant mechanism.

Even if you've got molecular orbitals with energy, it's very close to the Fermi energy, at least for short molecules.

And above 4 nanometers length, roughly speaking.

You usually see hopping taking over.

So at this point I'm going to finish and then the next lecture will have a look at trying to make something more sophisticated than the straight molecular wire.