Transcript 6_SHAKINESS_Fall_2009

Shaky
Nano Property #2:
All things shake, wiggle, shiver and move all
around at the nanoscale.
Brownian Motion
In both cases the fluorescent particles are 2 microns in diameter. The left picture
shows particles moving in pure water; the right picture shows particles moving in a
concentrated solution of DNA, a viscoelastic solution in other words. The movies
are 4 seconds of data, total; you can see a slight jump in the movie when it loops
around. http://www.deas.harvard.edu/projects/weitzlab/research/brownian.html
Basic Thermodynamics
Zeroth Law: If two systems are in thermal
equilibrium with a third system, they are in thermal
equilibrium with each other.
First Law: Energy in the universe is conserved
(it is also conserved in a closed system).
Second Law : Entropy increases
TEMPERATURE
What is Temperature anyway?
What is it a measure of ?
MOTION
In specific Scientific Terms: Temperature is a
measure of the average kinetic energy of the
particles in a system.
What is Energy?
Capacity to do Work. …
What does this mean?
Energy
Stored (Potential)
Chemical
Nuclear
Magnetic
Electrostatic
Mass
EM Radiation
Light
X-rays
microwaves
Motion (Kinetic)
Energetics of an Explosion
TNT
In what form is the energy?
Energetics of an Explosion
Bang!
In what form is the energy?
Heat is nano-scopic motion
Very, Very cold
Warm
Hot
Flow of Heat
Brownian Motion in a Fluid
Thermal Energy
Ethermal=1/2 k * Temperature
k = Botzmann’s constant
(1.38*10-23J/K)
Ethermal=1/2 kT
Average Energy of each degree of freedom in a
system.
At room Temperature, Ethermal=
4*10-21 J
or 0.025 eV
Fahrenheit,
Celsius, Kelvin
0
73
-273 -200
-459 -328
173
273
373
473
573
Kelvin
-100
-148
0
32
100
212
200
392
300
572
Celsius
Fahrenheit
Kinetic Energy
Ekinetic=1/2 (mass)*(velocity)2
Ekinetic= 1/2
2
mv
We can set the thermal energy of an object equal
to its kinetic energy to see how fast it is moving.
This is appropriate for relatively “free” particles.
Ekinetic=Ethermal
1/2 mv2 = 1/2 kT
1/2
v=(kT/m)
Thermally induced Kinetic Energy
v=(kT/m)1/2
(appropriate for a free particle)
Person
100kg
6*10-12m/s
Grain of Sand
10 mg
7*10-8m/s (10nm/s)
10 micron bead 4*10-12kg 20 microns/s
1 micron bead
4*10-15kg
Virus
5*10-19kg
Oxygen Molec. 5*10-26kg
700 micron/s
9 cm/s
270 m/s
Thermal Vibrations:
Carbon Nanotube
Bonding
Fat
Frep
r
Force between atoms: attractive and repulsive forces
Fnet=Fat+Frep
When Fnet=0, the atom is at its equilibrium position
Fnet=Fa+Fr=0
These forces are a function of position and
depend on the type of bonding
Potential Energy
How does bond energy relate to the rupture
force of a bond?
x
Transition State
0
Eb
xb
x
Eb=bond energy
xb=bond width
Potential Energy
How does bond energy relate to the rupture
force of a bond?
x
0
Eb
x
It Depends . . .
Effects of thermal energy on Bond Strength
Potential Energy
Thermal Energy affects the Dissociation
Constant and Bond Strength.
Thermal Energy aids the dissociation of a
bond.
0
x
Eb
kBT
Bond Strength: Boltzman Factor
What is the probability that
a bond will spontaneously
dissociate????
kT at room temperature = 0.025 meV
P=e-Eb/kT
The rate of dissociation
rd = f
-E
/k
T
b
B
e
Rate of
dissociation
Attempt frequency
Vibrational frequency of bond or
inverse relaxation time
Probability per
attempt
Bond Strength: Boltzman Factor
kb T at room temperature = 0.025 eV
P=e-Eb/kT
= 4 * 10 -21J
kb =1.38 × 10-23 m2 kg s-2 K-1
The rate of dissociation
rd = f
-E
/k
T
b
B
e
Rate of
dissociation
Attempt frequency
Vibrational frequency of bond or
inverse relaxation time
Probability per
attempt
Challenge Problem for the Brave
How much are atoms shaking at room temperature?
Lets take the case of a water molecule.
“Spring constant”
between Oxygen and
Hydrogen ~ 500 N/m.
O
H
k = 500 N/m
H
Espring = ½ k x2
Each degree of freedom has
½ kBT energy (on average)
kB = 1.38 × 10-23 m2 kg s-2 K-1
?
Give answer as
% of bond length