1. Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 11

2. Graphene Yet another amazing form of carbon Andre GeimKonstantin Novoselov Nobel Prize in Physics 2010 Univ. of Manchester, UK

3. Carbon: the Element of Life Has unique flexibility for bonding and ability to make complex compounds All life forms on Earth, from viruses to complex mammals (including humans) are based on carbon chemistry. The Tobacco Mosaic Virus contains a single strand of RNA, about 0.1 mm long This complex mammal contains about 3 billion miles of DNA.

4. Even pure carbon can be present in a variety of forms: Graphene (top left) is a 2D honeycomb lattice of carbon atoms. Graphite (top right) can be viewed as a stack of graphene layers. Carbon nanotubes are rolled-up cylinders of graphene (bottom left). Fullerenes C 60 (bottom right) are molecules consisting of wrapped graphene by the introduction of pentagons on the hexagonal lattice. (From Castro-Neto et al. 2006) Diamond vs. graphite Cubic Lattice, Very tight, inflexible Honeycomb Sheets that easily slide (pencil)

5. How Geim and Novoselov produced it They used Scotch tape to repeatedly split graphite crystals into increasingly thinner flakes Then placed the flakes to a silicon dioxide substrate to prevent them from scrolling You could do this as well (if only you knew what to look for)

6. Graphene structure A single layer of carbon atoms tightly packed into a honeycomb lattice Electron dispersion (dependence of electron energy from its momentum) Note linear dependence E(p) near E = 0!! What does it mean?

7. Ultrahigh mobility, low resistance (like in copper!) Unique optical properties (absorption independent on wavelength) Unique magnetic properties Penetration through energy barriers p E Electron Dynamics in Graphene

8. Potential applications Transistors Integrated circuits Lasers Detectors memory

9. Work Energy Theorem

10. A person is pulling a crate of mass M along the floor with a constant force F over a distance d. The coefficient of friction is . (a)Find the work done by the force F on the crate. (b)Same if F changes as F 0 (1+x 2 /d 2 ). (c)Find the work done by the force of friction on the crate (F is constant). (d)Find the net work done on the crate if the crate is pulled with a constant velocity. (e)Find the final velocity of the crate if the crate is pulled with a non-zero acceleration starting from the rest. M

11. A block of mass m starts at the top of an inclined plane. The coefficient of friction between the plane and the block is . Assuming the block slides down the plane calculate the work done by each force.

12. x

13. Problem 2 p.122 A 3 slug mass is attached to a spring which is pulled out one foot. The spring constant k is 100 pounds/ft. How fast will the mass be moving when the spring is returned to its unstretched length? (Assume no friction.)

14. Problems from handout

15. Problem 3 A 5.00 kg block is moving at v 0 =6.00 m/s along a frictionless, horizontal surface toward a spring with constant k=500 N/m that is attached to a wall. a)Find the maximum distance the spring will be compressed. b)If the spring is to compress by no more than 0.150 m, what should be the maximum value of v 0 ?

16. Have a great day!