Download Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 11
Graphene
Yet another amazing form of
carbon
Nobel Prize in Physics 2010
Andre Geim
Konstantin Novoselov
Univ. of Manchester, UK
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.
Even pure carbon can be present
in a variety of forms:
Diamond vs.
Cubic
Lattice,
Very tight,
inflexible
graphite
Honeycomb
Sheets that
easily slide
(pencil)
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
C60 (bottom right) are molecules consisting of wrapped graphene by the
introduction of pentagons on the hexagonal lattice. (From Castro-Neto et al. 2006)
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)
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?
Electron Dynamics in Graphene
• Ultrahigh mobility, low
resistance (like in copper!)
• Unique optical properties
(absorption independent
on wavelength)
E
• Unique magnetic
properties
p
• Penetration through
energy barriers
Potential applications
•
•
•
•
•
Transistors
Integrated circuits
Lasers
Detectors
memory
Work Energy Theorem

r2

 mV
W   Ftotaldr 

2
r1
x2 y 2
F

total
x
x1 y1
2
final
dx 
x2 y 2
F

total
y
x1 y1
dy 
2
initial
mV

2
mV
2
final
2
2
initial
mV

2
M
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 F0(1+x2/d2).
(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.
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.


Hooke' s Law : F  k ( x  x0 )i
x0 is unstreched position
x
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.)
Problems from handout
Problem 3
A 5.00 kg block is moving at v0=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 v0?
Have a great day!