Dr. Aniruddha Chakraborty

Course Details:                                                                           

The course will provide an introduction to nanoscience. Some of the fundamental concepts used to study the world at the nanoscale will be discussed in detail. Understanding of these concepts is fundamental in understanding how nanoscale interactions & phenomena differ from those in our common macroscale world. Finally this course will provides specific study of the application of nanotechnology to different areas of science.

Course Outline

• Big picture and principles of the small world.

• Why ‘the smaller, the better’?

•  Introduction to Nanoscale physics.

• Nanoscale Fluid Mechanics, Nanoscale Heat transfer.
  

• Nanobiology, Molecular motors.

References

1. Introduction to Nanoscience : S. M. Lindsay, Oxford 2010.

2. Nanotechnology: Understanding small systems : Rogers, Pennathur & Adams, CRC press 2008.

3. Introductory Nanoscience : Masaru Kuno, Garland Science 2011.

4. Quantum Mechanics for Nanostructures : Vladimir V. Mitin, Dimitry I. Sementsov & Nizami Z. Vagidov, Cambridge, 2010.

5. Nanophysics and Nanotechnology: An introduction to the modern concepts in Nanoscience: Edward L. Wolf, Wiley-VCH, 2011.

        6. Introductory Quantum Mechanics : Richard L. Liboff, Addison-Wesley, 1993.

7. Foundations of Nanomechanics, A. N. Clealand, Springer, 2003.

8. Nano Devices, 2D electron solvation & curve crossing problems: A. Chakraborty, Lambert, 2010

Marks Distribution

Assignments 30%, quizzes 20% & final exam. 50%.

Tentative Lectures



Assignment 1 Questions

Do calculations for three different sizes of a nanostructure, as mentioned in the class.

(a) An estimate of the number of atoms in a nanostructure using a unit cell approach.

(b) An estimate of the number of surface atoms in a nanostructure using a unit cell approach.

(c) One/more conclusions ?



Assignment 2 Questions

Do a literature survey on 'quasicrystal' and submit  a short note on quasicrystal. Mention where quasicrystal is different from amorphous, polycrystalline and crystalline solids.

Assignment 3 Questions

Charles-Augustin de Coulomb, French physicist best known for the formulation of Coulomb's Law, which states that the force between two electrical charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Write a short note on how did Coulomb arrive at his law ?



Assignment 4 Questions

Let us consider a "x" diameter metal sphere embedded in a dielectric medium (epsilon =20). Find the charging energy of the sphere ?

Case 1: x = 3 nm. Case 2: x = 30 nm & x = 300 nm.

Any conclusion ?



Reading Assignment 1

Explained: Phonons - When trying to control the way heat moves through solids, it is often useful to think of it as a flow of particles: by David L. Chandler, MIT News OfficeLink: http://web.mit.edu/newsoffice/2010/explained-phonons-0706.html.

Reading Assignment 2

Don't define nanomaterials: An interesting article by Andrew D. Maynard. Reference: Nature, 475, 31 (07 July 2011). DOI:10.1038/475031aLink: http://www.nature.com/nature/journal/v475/n7354/full/475031a.html.



Quiz 1 Questions

1. Nanometer is a magical point on the dimension scale – why?                                                  

2. What is the difference between nanoscience and nanotechnology?                                     

3. Name two things you are familiar with that are roughly 1 millimeter in size. Name something that is approximately 1 micrometer in size. Name something that is 1 nanometer in size.                       

4. What is the difference between quantum dot, quantum wire and quantum well?                   

 5. Does really surface area increase when size is reduced? Explain with simple examples.    

6. When & where Feynman delivered his lecture on ‘nano’ & what is the name of that lecture?

7. Nanotechnology is new but research in nanometer scale is not new – explain.                     

8. Provide a brief synopsis of the most famous debate on nanotechnology/nanobots.                                                                                               

9. Explain the role of top down and bottom up approaches in understanding nanosystems.      

10.“Till today, picotechnology and femtotechnology do not make sense in the way that    nanotechnology does” – explain.  

Quiz 2 Questions

1. Explain what the size of the exciton Bohr radius means for achieving quantum confinement. What systems are easiest for achieving this effect? Explain why?   

2. Can ‘excitons’ be seen in the electronic absorption spectrum of bulk semi-conductors? Give explanation.                                                               

3. True or False? Also give explanations in support of your answer.

(a) Once an energy band is formed its width is proportional to the number of atoms in the solid.

(b) The band gap of a quantum dot is directly proportional to its size.                  

(c) A quantum dot containing thousands of atoms can be used to trap a single free electron – in effect creating a gigantic, artificial hydrogen atom.                                                       

(d) When numerous atoms are brought into close proximity, only the highest occupied energy sub-level forms a band.                                          

(e) Quantum confinement relates only to those electrons that would otherwise be mobile - the conduction electrons. 

Final Exam. Questions

1. Can the total energy and linear momentum of a particle moving in one dimension in a constant potential field be measured consecutively with no uncertainty in the values obtained ? Explain.  

2. Consider the Schrodinger equation with a periodic potential. Are the eigenfunctions of this equation necessarily periodic ? Justify your answer.                                                                                                                                

3. Which are faster carrier of heat through a nano size metal: electrons or phonons ? Explain.

4. Consider two Hermitian operators A and B, which satisfy the commutation relation [A,B] = iħ.Suppose a system is in an eigenstate of A. What can be said of the probability distribution related to B ? Explain.

5. What is Optical Tweezer ?  

6. One dimensional box containing an electron suffers an infinitesimal perturbation and emits a photon of frequency hn = 3 E₁ with E_n= n² E₁, where E₁ denotes the ground state of the particle. A student conclude that the electron was in the state f₂ prior to perturbation. Is he correct ? Justify.

7. When you heat a solid nano-material, do the atoms within it vibrate with grater amplitude or greater frequency ? Explain.

8. A particle in one dimension is in the energy eigenstates  f(k₀)=A cos(k₀x). Ideal measurement of energy finds the value E=ħ²k₀²/(2m). What is the state of the particle after measurement ? Explain.

9. What is photonic crystal ? What is photonic band gap ?

10. Give a brief explanation for why the electrical resistance of a nano size solid tend to increase as it gets hotter.                                

11. Why understanding the concept of ‘density of states’ is important in nanoscience ? Explain.

12. What is phonon ? What characteristic must an atomic lattice have for it to support optical phonons ?                                                     

13. Suppose that in a sample of 1000 electrons, each has a wavefunction Y(x,t) = sin(x) e^-iwt. Measurements are made (at a specific time t = t’) to determine the location of electrons  in the sample. Approximately how many electrons will be found in the interval -1 ≤ x ≤1 ?              

14. What is the working principle of Light Emitting Diode (LED) ?                                                                                                                      

15. Define effective mass of a particle in an atomic lattice.

16, A free particle of mass m moving in one dimension is known to be in the initial state Y(x,0)= sin(k₀x). Suppose that p is measured at t = 3 sec and the value of hk₀ is found. What is Y (x,t) at t > 3 sec ?

17. (a) What is buckling ? (b) What is the difference between buckling and bending ? (c) Write at least one possible application of buckling in the area of nanoscience. (d) Explain the potential energy diagram of a nano rod under compression. (e) Using this diagram explain why it is practically not possible for a nano rod to go from one buckled state to another under sufficiently high compression.                                                                                                                                  

18. (a) What is a single molecule transistor? (b) What is a single electron transistor ? (c) What are the possible differences between single molecule transistor and single electron transistor ? (d) Discuss the possible mechanism of electron transport in the case of single C₆₀ transistor. (e) Explain why current increases with the increase in bias voltage between the source and drain electrode ? (f) In case of single C₆₀ transistor, is electron transport rate same as the oscillation frequency of the center of mass of C₆₀ in between two electrodes ? Explain. (g) What is the origin of 5 meV vibrational quantum in current vs. voltage plot at 1.5 K for a single C₆₀ transistor.

Few More Interesting  Questions

1. The suppression of a systems melting point is one of the known property of nano-scale materials (semiconductor & metal). Can you think of any potential applications that exploit this property ?

2. Provide examples of some companies that are currently producing nano-related products.

3. Before 1998, there were very few Universities/Institutes dedicated to Nano-science. Today, there are a number of Institutions/Universities dedicated to Nano-science. Can you find a few of these Universities/Institutions ?

4. Assume Drexler is right and one "assembler" can assemble a million of atoms within a second. Roughly how long would it take for one of these assemblers to put together a cricket ball ? Make assumptions where necessary and state your assumptions explicitly.

5. Measuring distances on the nanometer scale is an important task for a number of scientific investigations. Find at least one examples.

6. More recently, colloidal nanoparticles have been used as molecular rulers, do you have any idea of how the technology works ?

7. Having seen many applications of low dimensional materials, attempt to devise an original application of wells, wires or dots (or any other nano-system). Describe your application, state why it has advantages over bulk analogues, and explain how you intend to make such a device.

8. Read about Magnetotactic Bacteria that naturally contain magnetic particles. Find out how these bacteria synthesize nanoparticles. Then ask yourself why they would want them in the first place.

9. Provide examples of some companies that are currently producing nano-related products.

10. Does the effective band gap of a low dimensional semiconductor increase with degree of confinement (the band gap is akin to the HOMO-LUMO gap of a molecular system) ?

11. What is dark exciton ?

12. Consider the well-known progression of colours possessed by ensembles of different-sized colloidal CDSe quantum dots. The samller particle appear yellow. Larger one appear red. Think about why small diameter ensembles appear yellow while larger-diameter ensembles appear red. Similarly, it is well known that gold nanoparticles generally have a distinct ruby red colour. By contrast, aggregated gold ensembles appear blue to the eye. Think about the origin of these colours as well.

13. There is considerable interest in the community in going beyond the generic classes of nanosctructures. For example there is interest in combining individual quantum dots to make so called quantum dot "molecules". Alternatively, one can make more extended structures, leading to artificial "solids" sometimes called superlattices. Find examples of each in the literature.

14. Find two examples in the current literature, where materials are said to be in any one of the various confinement regimes, described in the class.

15. Explain what the size of the exciton Bohr radius mean for achieving quantum confinement. What systems are easier for achieving this effect ?

16. Find an example from the literature where the surface to volume ratio is invoked to explain some special property of nanostructure.

17. What are the some of the broader moral and ethical implications of nanoscience and nanotechnology ?

18. One of the major concerns these days with nanoscience and nanotechnology has to do with health risks. There are those who think that all nano-related research should be stopped until its health risks have been fully evaluated. Can you think about the possible 'origin' of these health risks ?

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