Nanoscience

Question 1

What graph describes the Lenard Jones potential and which parts describe its attactive and repulsive parts.

Answer 1

Question 2

What is the relationship between force and potential?

Answer 2

Force is the negative derivative of potential.

Question 3

What is the morse potential and what is it used for?

Answer 3

The Morse potential is used to approximate the potential energy variation for two neutral atoms.

Question 4

Explain the origin of the repulsive and attractive components of the Lennard Jones potential.

Answer 4

The r^-6 term models the attractive force between the atoms arising from the long range van der Walls force.

The r^-12 term accounts for the repulsive interactions due to the short range repulsion from the overlapping of electron orbitals.

Question 5

Explain the van der Walls force

Answer 5

• Instantaneous dipoles are constantly forming in atoms.
• Van der Walls forces are the interactions between these instantaneous dipoles.

Question 6

What is meant by a covalent and an ionic bond?

Answer 6

A covalent bond involves the sharing of electron pairs between atoms. These electron paris involve the overlap of electron orbitals.

Ionic bonding involves the transfer of charge so there is an electrostatic force of attraction between two oppositely charged ions.

Question 7

What is the difference between inertia and viscosity?

Answer 7

Inertia is the ability of the fluid to move out of the way quickly enough.

Vicosity is the ‘gooiness’ of a fluid - its a measure of the resistance to flow

Question 8

What is a random walk?

Answer 8

Atoms and molecules are associated with translational, vibrational, and rotational motions. The random motion of atoms can be described as a random walk.

One such example is Brownian motion.

Question 9

What is the mean square displacement of an atom/molecule?

Answer 9

The mean of the displacements squared. (So that the mean isn’t zero)

Question 10

How does the mean square displaceent vary with time for a random walk?

Answer 10

The mean square displacement varies linearly with time.

Question 11

What is the de Broglie relationship?

Answer 11

The wavelength of a particle is inversely proportional to its momentum.

Question 12

What is the formula for energy separation in an infinite 1D potential well?

What simple conditions are used to find the formula?

Answer 12

There must be a whole number of half wavelengths in the length of the well. It must go to zero at the boundaries of the well.

The energy is purely kinetic energy.

Question 13

What is the relationship between wavefunction and probability?

Answer 13

Question 14

What is the time-independent 1D Schrodinger equation?

Answer 14

Question 15

What are the boundary conditions for a particle in an infinite box

Answer 15

The value of the wavefunction must be zero at x=0 and x=L.

Question 16

Explain what is meant by quantum mechanical tunnelling?

Answer 16

Classically a particle whose energy is less than the barrier height could never be found on the right hand side of the barrier.

Quantum mechanically, not only is there a finite probability of finding the particle on the right hand side of the barrier but the particle can also exist inside the barrier.

Question 17

What is the relationship between tunnel current and barrier width?

Answer 17

Question 18

What is the decay length?

Answer 18

Question 19

Why can’t an optical microscope resolve atoms?

Answer 19

When the size of an object becomes comparable to the wavelength of light used to image it then diffraction plays a key role in how the photons of light are scattered by the object.

Question 20

How is tunnelling exploited in the STM?

Answer 20

A sharp metal tip is brought to within a nanometre of the surface of a conducting sample with a boltage between the tip and sample.

Even though the tip and sample aren’t in electrical contact, a current can still flow due to electrons quantum mechanically tunnelling across the vacuum gap.

Question 21

Explain constant height mode for STM

Answer 21

In constant height mode the tip is canned back and forth across the surface whilst its height is kept constant.

As the tip is scanned, the tunnel current is measured and a map of the surface is generated from the variation in current.

Question 22

Explain constant current mode for STM

Answer 22

The height of the tip is varied as the tip moves across the surface so that the tunnel current is kept constant.

A map of the surface is generated from the variation in tip position.

Question 23

How does contact AFM operate?

Answer 23

In contact AFM the tip is dragged across the surface of the sample and the contours of the surface are measured using the deflection of the cantilever.

Question 24

How does non-contact AFM operate?

Answer 24

The cantilever is oscillated at its resonat frequency. As the top is moved toweards the surgace the presence of a force gradient effectively modifies the spring constant of the cantilever by providing a damping force.

Question 25

What formula describes the change in frequency for non-contact AFM?

Answer 25

F’ is the force potential

Question 26

What is the hopping rate expression?

Answer 26

Question 27

What is diffusion-limited aggregation?

Answer 27

As atoms are not free to diffuse around the edge of the aggregate they remain locked in place. This is because the interaction of the abosrbates is strong so an adsorbate diffusing across a surface meets a growing island but cannot diffuse to a lower energy bonding site because the interaction with the edge of the island pins it in place.

Question 28

What is attachment in the context of crystal growth?

Answer 28

As atoms attach to a seed an island grows. Generally atoms want to form bonds to lower the energy of the system.

Question 29

What is detachment in the context of crystal growth?

Answer 29

There is a finite - and at relatively high temperatures, rather large probability for an atom to detach.

Question 30

Define Quantum Confinement.

Answer 30

Quantum confinement refers to the restriction of the electron to a particular region of space.

In the 1D particle in a box model this means that the electron wavefunction must go to zero at the edges of the box.

This imposes certain allowed values for the wavelength and thus the energy of the electronic standing waves in the box.