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DOI: 10.22184/1993-8578.2021.14.2.136.141
How can we see something hidden to the human eye and is not even visible in the best optical microscope? How can we observe atoms and molecules? How to view the objects of wild nature of nanoscale in details under normal conditions, in air or in liquid? An atomic force microscope comes to help ing us. We will talk about how it is arranged, which it consists of how it works and how it gets images of the nanoworld.
How can we see something hidden to the human eye and is not even visible in the best optical microscope? How can we observe atoms and molecules? How to view the objects of wild nature of nanoscale in details under normal conditions, in air or in liquid? An atomic force microscope comes to help ing us. We will talk about how it is arranged, which it consists of how it works and how it gets images of the nanoworld.
Теги: atomic-force microscope biological objects nanoscale nanoworld optical microscope атомно-силовой микроскоп биологические объекты наномасштаб наномир оптический микроскоп
LOOK INTO THE NANOWORLD: IN CONTACT
I.V.Yaminskiy, Doct. of Sci. (Physics and Mathematics), Prof. of Lomonosov Moscow State University, Physical and Chemical departments, Director of Advanced Technologies Center, Leading Sci. of INEOS RAS
How can we see something hidden to the human eye and is not even visible in the best optical microscope? How can we observe atoms and molecules? How to view the objects of wild nature of nanoscale in details under normal conditions, in air or in liquid? An atomic force microscope comes to help ing us. We will talk about how it is arranged, which it consists of how it works and how it gets images of the nanoworld.
The atomic force microscope was invented in 1986 by Gerd Binnig, Kelvin Quat and Christoph Gerber [1]. Now it has become the most important and most popular tool in the family of scanning probe microscopes. Just 5 years before this date, the first of the probe microscopes was invented – a scanning tunneling microscope. In the same 1986, Gerd Binnig, co-author of the atomic-force microscope, together with Heinrich Rohrer, was awarded the Nobel Prize in Physics for invention of the tunneling microscope [2].
Atomic force microscope appeared as a modification of the tunneling microscope in order to measure forces in tunneling contact. It is interesting that this could have happened more than 150 years ago after invention of the phonograph by Thomas Alva Edison, where movement of the needle on the surface relief was converted into sound. In the atomic force microscope the probe moves like in a gramophone player tracking all irregularities by a trajectory that repeats all the bends of the sample. As a result of movement of the gramophone needle we hear a melody, the movement of the atomic force microscope needle gives rise to an image. Getting these trajectories one after another in the atomic force microscope, we gradually get a map of the peculiarities of the entire scanned sample area. We can see atoms on the surface, DNA molecule, proteins, viruses, bacteria and even individual cells.
Forces arise at the point of the probe-sample contact in the atomic force microscope. In order to better understand the force acting on the probe, imagine that the probe is placed on an elastic spring and scans the surface.
At low distances about 10 nm a noticeable force of attraction arises between all bodies. This is the Van der Waals power. It has an electromagnetic nature: the closer to the surface, the greater the value of this force. For two atoms or molecules the energy of attraction is inversely proportional to the 6th degree of the distance between their centers R, and for the force we obtain F~1/R7.
If you sum up all the pair forces between the probe molecules and the sample then we define the Van der Waals force for this case as well. When the probe comes in contact with the sample surface the Van der Waals power is maximum. An additional force appears during the formation of contact – the strength of adhesion. This force may be caused by various reasons. For example, the capillary forces arise. The force of adhesion can also appear due to the electrification of the surface of the probe and sample. This force can be observed: if a toy balloon rubs against one’s hair, it is electrified and starts sticking to the surfaces. For stability of the atomic force microscope operation, the probe is additionally pressed to the sample. In this case, still another force acting on the probe arises – the force of elasticity.
So, there are three forces, and they all will press the probe down. But the probe does not fall through the surface, it means there is another force that balances all the three previous ones. This is a contact force or support reaction. What is the nature of this force? This is the most difficult and mysterious question of the atomic force microscopy.
Remember that the probe should be fixed on an elastic spring. As a rule, this spring is made in the form of an elastic cantilever – a beam fixed on one end. At its free end there is the probe. This design is called cantilever (Fig.2).
Cantilivers are used not only in the atomic force microscopy. In aircraft construction it is a plane wing, so Junkers from biplan moved to a monoplane (Fig.3a). Drawbridges in Saint-Petersburg are cantilever bridges (Fig.3b).
The element performed by the figure skating world champion A.Trusova is also a cantilever (Fig.3c).
During the scan, the probe slides over the sample surface (Fig.4a). How do we determine the trajectory of the probe? To do this, the light from the laser is focused on the cantilever free end, and a position of the reflected ray is determined using the photodetector. When the cantilever moves by dz value, the light spot on the photodiode is shifted to a significantly greater distance, which is by 2L/l times more. Here, L is a path of the reflected light, l is a length of the cantilever. Usually it is 1,000 times. It is for 100 microns cantilever, a distance from the cantilever to the photodiode is 5 cm. The optical system should register only microns if the relief changes in nanometers.
Photodiode has four segments – A, B, C, D (see Fig.4b). If you measure the total signal on all segments simultaneously, we get the intensity of the light falling onto the photodiode. While scanning, the intensity is almost constant, and when setting up the optical system, we need to achieve that the intensity of light on the photodiode is maximum.
If the cantilever moves up and down, the spot on the photodiode is also moving up and down and therefore the signal (A + B) – (C + D) indicates the height of the relief.
We can also measure the friction force by an atomic force microscope. Those are friction properties of the surface. The friction force is directed horizontally along the sample surface. This force leads to rotation the cantilever around its axis and the horizontal shift of the light spot on the photodiode.
That is, the signal (A + C) – (B + D) is nothing else but the friction force or the friction coefficient of the sample surface. In order to properly measure the friction, it is necessary that the direction of scanning is perpendicular to the longer axis of the cantilever. You need to remember this!
Hence, A + B + C + D is the light intensity, (А + В) – (С + В) – deflection of the cantilever and (A + C) – (B + D) – friction.
The last two signals play an important role while scanning. We will simply call them "deflection" and "friction".
Quite often, while scanning in the atomic force microscope we move the sample, not the probe. It is more convenient because the laser system is connected with the probe.
Therefore, the sample is placed on a piezoceramic manipulator, which must move the sample with an accuracy of at least 0.001 nm. It is 100 times less than the smallest atom of hydrogen. If so, then we can scan the relief of one atom.
In the atomic force microscope the feedback is used. If the relief has become higher, the sample is moved downward. As a result, the cantilever does not move vertically and the force of its pressure on the surface remains constant. Therefore, we can provide a delicate scanning at constant force. It means the constant force mode.
How does the feedback work? If the probe began to rise on the slope of the protrusion, the deflection signal immediately indicates that the sample should be moved downward. This requires precision electronics. The signal from the photodiode (A + B) – (C + D) enters a sensitive amplifier where it is compared with the earlier preset value (so called reference value), an error signal is obtained and is amplifies and fed to a piezomanipulator in the correct polarity so that the feedback is negative. Such a regulator is called proportional regulator.
We can continuously summarise the error signal: the error varies from a positive value to the negative value and the current sum has a definite value. However, if we have a small error that a proportional regulator cannot track down then the amplified signal of the summarised error will return the probe into exactly defined position. It is an integral regulator because the integral means a continuous summation.
If a sharp spike appears and the first two techniques do not help, then you need to measure a change in the error signal – its mathematical derivative, and in that case we will get a differential regulator.
Thus, we can build one regulator with three links and get a proportional-integral-differential regulator – PID controller.
PID regulators are used everywhere: for example, when flying a winged rocket above a rough terrain. The sensor records the height of the flight, and feedback and the adjustment system holds the selected rocket course.
And now let us recollect our question: what is this contact force that holds the sample on the surface? This force plays a key role in atomic force microscopy. First of all, we would like to control and reduce it, because it is applied at the point of contact or to the same atom which is located at the top of the probe. If the contact force is large, the probe and sample are deformed, and we begin to see the surface not so clear.
This is the force of exchange interaction that appears from the Pauli exclusion principle. At one spatial point there can be not more than two electrons, and these two electrons must have different spin – the moment of the amount of movement.
Do you think this principle applies to atomic force microscopy only? We, our table, chair and the microscope itself would have long fallen through the floor if this principle would not work in ALL cases. Indeed, in all cases.
The story "Look into Nanoworld: In contact" you can watch and listen on the Internet link https://youtu.be/rhigj5eylsg. There we added animation and live speech. Pleasant and useful viewing!
ACKNOWLEDGEMENTS
The study was completed with the financial support of the RFBR and the London Royal Society No. 21-58-10005, RNF, Project No. 20-12-00389, RFBR, Project No. 20-32-90036. ■
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
I.V.Yaminskiy, Doct. of Sci. (Physics and Mathematics), Prof. of Lomonosov Moscow State University, Physical and Chemical departments, Director of Advanced Technologies Center, Leading Sci. of INEOS RAS
How can we see something hidden to the human eye and is not even visible in the best optical microscope? How can we observe atoms and molecules? How to view the objects of wild nature of nanoscale in details under normal conditions, in air or in liquid? An atomic force microscope comes to help ing us. We will talk about how it is arranged, which it consists of how it works and how it gets images of the nanoworld.
The atomic force microscope was invented in 1986 by Gerd Binnig, Kelvin Quat and Christoph Gerber [1]. Now it has become the most important and most popular tool in the family of scanning probe microscopes. Just 5 years before this date, the first of the probe microscopes was invented – a scanning tunneling microscope. In the same 1986, Gerd Binnig, co-author of the atomic-force microscope, together with Heinrich Rohrer, was awarded the Nobel Prize in Physics for invention of the tunneling microscope [2].
Atomic force microscope appeared as a modification of the tunneling microscope in order to measure forces in tunneling contact. It is interesting that this could have happened more than 150 years ago after invention of the phonograph by Thomas Alva Edison, where movement of the needle on the surface relief was converted into sound. In the atomic force microscope the probe moves like in a gramophone player tracking all irregularities by a trajectory that repeats all the bends of the sample. As a result of movement of the gramophone needle we hear a melody, the movement of the atomic force microscope needle gives rise to an image. Getting these trajectories one after another in the atomic force microscope, we gradually get a map of the peculiarities of the entire scanned sample area. We can see atoms on the surface, DNA molecule, proteins, viruses, bacteria and even individual cells.
Forces arise at the point of the probe-sample contact in the atomic force microscope. In order to better understand the force acting on the probe, imagine that the probe is placed on an elastic spring and scans the surface.
At low distances about 10 nm a noticeable force of attraction arises between all bodies. This is the Van der Waals power. It has an electromagnetic nature: the closer to the surface, the greater the value of this force. For two atoms or molecules the energy of attraction is inversely proportional to the 6th degree of the distance between their centers R, and for the force we obtain F~1/R7.
If you sum up all the pair forces between the probe molecules and the sample then we define the Van der Waals force for this case as well. When the probe comes in contact with the sample surface the Van der Waals power is maximum. An additional force appears during the formation of contact – the strength of adhesion. This force may be caused by various reasons. For example, the capillary forces arise. The force of adhesion can also appear due to the electrification of the surface of the probe and sample. This force can be observed: if a toy balloon rubs against one’s hair, it is electrified and starts sticking to the surfaces. For stability of the atomic force microscope operation, the probe is additionally pressed to the sample. In this case, still another force acting on the probe arises – the force of elasticity.
So, there are three forces, and they all will press the probe down. But the probe does not fall through the surface, it means there is another force that balances all the three previous ones. This is a contact force or support reaction. What is the nature of this force? This is the most difficult and mysterious question of the atomic force microscopy.
Remember that the probe should be fixed on an elastic spring. As a rule, this spring is made in the form of an elastic cantilever – a beam fixed on one end. At its free end there is the probe. This design is called cantilever (Fig.2).
Cantilivers are used not only in the atomic force microscopy. In aircraft construction it is a plane wing, so Junkers from biplan moved to a monoplane (Fig.3a). Drawbridges in Saint-Petersburg are cantilever bridges (Fig.3b).
The element performed by the figure skating world champion A.Trusova is also a cantilever (Fig.3c).
During the scan, the probe slides over the sample surface (Fig.4a). How do we determine the trajectory of the probe? To do this, the light from the laser is focused on the cantilever free end, and a position of the reflected ray is determined using the photodetector. When the cantilever moves by dz value, the light spot on the photodiode is shifted to a significantly greater distance, which is by 2L/l times more. Here, L is a path of the reflected light, l is a length of the cantilever. Usually it is 1,000 times. It is for 100 microns cantilever, a distance from the cantilever to the photodiode is 5 cm. The optical system should register only microns if the relief changes in nanometers.
Photodiode has four segments – A, B, C, D (see Fig.4b). If you measure the total signal on all segments simultaneously, we get the intensity of the light falling onto the photodiode. While scanning, the intensity is almost constant, and when setting up the optical system, we need to achieve that the intensity of light on the photodiode is maximum.
If the cantilever moves up and down, the spot on the photodiode is also moving up and down and therefore the signal (A + B) – (C + D) indicates the height of the relief.
We can also measure the friction force by an atomic force microscope. Those are friction properties of the surface. The friction force is directed horizontally along the sample surface. This force leads to rotation the cantilever around its axis and the horizontal shift of the light spot on the photodiode.
That is, the signal (A + C) – (B + D) is nothing else but the friction force or the friction coefficient of the sample surface. In order to properly measure the friction, it is necessary that the direction of scanning is perpendicular to the longer axis of the cantilever. You need to remember this!
Hence, A + B + C + D is the light intensity, (А + В) – (С + В) – deflection of the cantilever and (A + C) – (B + D) – friction.
The last two signals play an important role while scanning. We will simply call them "deflection" and "friction".
Quite often, while scanning in the atomic force microscope we move the sample, not the probe. It is more convenient because the laser system is connected with the probe.
Therefore, the sample is placed on a piezoceramic manipulator, which must move the sample with an accuracy of at least 0.001 nm. It is 100 times less than the smallest atom of hydrogen. If so, then we can scan the relief of one atom.
In the atomic force microscope the feedback is used. If the relief has become higher, the sample is moved downward. As a result, the cantilever does not move vertically and the force of its pressure on the surface remains constant. Therefore, we can provide a delicate scanning at constant force. It means the constant force mode.
How does the feedback work? If the probe began to rise on the slope of the protrusion, the deflection signal immediately indicates that the sample should be moved downward. This requires precision electronics. The signal from the photodiode (A + B) – (C + D) enters a sensitive amplifier where it is compared with the earlier preset value (so called reference value), an error signal is obtained and is amplifies and fed to a piezomanipulator in the correct polarity so that the feedback is negative. Such a regulator is called proportional regulator.
We can continuously summarise the error signal: the error varies from a positive value to the negative value and the current sum has a definite value. However, if we have a small error that a proportional regulator cannot track down then the amplified signal of the summarised error will return the probe into exactly defined position. It is an integral regulator because the integral means a continuous summation.
If a sharp spike appears and the first two techniques do not help, then you need to measure a change in the error signal – its mathematical derivative, and in that case we will get a differential regulator.
Thus, we can build one regulator with three links and get a proportional-integral-differential regulator – PID controller.
PID regulators are used everywhere: for example, when flying a winged rocket above a rough terrain. The sensor records the height of the flight, and feedback and the adjustment system holds the selected rocket course.
And now let us recollect our question: what is this contact force that holds the sample on the surface? This force plays a key role in atomic force microscopy. First of all, we would like to control and reduce it, because it is applied at the point of contact or to the same atom which is located at the top of the probe. If the contact force is large, the probe and sample are deformed, and we begin to see the surface not so clear.
This is the force of exchange interaction that appears from the Pauli exclusion principle. At one spatial point there can be not more than two electrons, and these two electrons must have different spin – the moment of the amount of movement.
Do you think this principle applies to atomic force microscopy only? We, our table, chair and the microscope itself would have long fallen through the floor if this principle would not work in ALL cases. Indeed, in all cases.
The story "Look into Nanoworld: In contact" you can watch and listen on the Internet link https://youtu.be/rhigj5eylsg. There we added animation and live speech. Pleasant and useful viewing!
ACKNOWLEDGEMENTS
The study was completed with the financial support of the RFBR and the London Royal Society No. 21-58-10005, RNF, Project No. 20-12-00389, RFBR, Project No. 20-32-90036. ■
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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