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ShakyNano 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 ThermodynamicsZeroth 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
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.
TEMPERATURE
What is Energy?Capacity to do Work. …
What does this mean?
Energy
Stored (Potential) Chemical Nuclear
MagneticElectrostatic
Mass
EM Radiation Light X-raysmicrowaves
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 motionVery, Very cold
Warm
Hot
Flow of Heat
Brownian Motion in a Fluid
Thermal EnergyEthermal=1/2 k * Temperature
k = Botzmann’s constant (1.38*10-23J/K)
Ethermal=1/2 kTAverage Energy of each degree of freedom in a system.
At room Temperature, Ethermal= 4*10-21 J
or 0.025 eV
Fahrenheit, Celsius, Kelvin
Kelvin
3000 100-200 -100-273 200
273 373173730 473 573
57232 212-328 -148-459 392
CelsiusFahrenheit
Kinetic Energy
Ekinetic=1/2 (mass)*(velocity)2
Ekinetic= 1/2 mv2
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 kTv=(kT/m)1/2
Thermally induced Kinetic Energy
v=(kT/m)1/2 (appropriate for a free particle)
Person 100kg 6*10-12m/s
Grain of Sand 10 g 7*10-8m/s (10nm/s)
10 micron bead 4*10-12kg 20 microns/s
1 micron bead 4*10-15kg 700 micron/s
Virus 5*10-19kg 9 cm/s
Oxygen Molec. 5*10-26kg 270 m/s
Thermal Vibrations:Carbon Nanotube
Bonding
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
FrepFat
How does bond energy relate to the rupture force of a bond?
Pot
enti
al E
nerg
y
xEb=bond energy
x
xb
xb=bond width
Transition State
Eb
0
How does bond energy relate to the rupture force of a bond?
Pot
enti
al E
nerg
y
xEb
x
0
It Depends . . .
Effects of thermal energy on Bond StrengthP
oten
tial
Ene
rgy
xEb
kBT
Thermal Energy affects the Dissociation Constant and Bond Strength.
Thermal Energy aids the dissociation of a bond.
0
Bond Strength: Boltzman FactorWhat is the probability that a bond will spontaneously dissociate????
P=e-Eb/kTkT at room temperature = 0.025 meV
The rate of dissociation
rdfe-Eb/kBT
Attempt frequencyVibrational frequency of bond orinverse relaxation time
Probability per attempt
Rate of dissociation
Bond Strength: Boltzman Factor
P=e-Eb/kT
kb T at room temperature = 0.025 eV
= 4 * 10 -21J
kb =1.38 × 10-23 m2 kg s-2 K-1
The rate of dissociation
rdfe-Eb/kBT
Attempt frequencyVibrational frequency of bond orinverse relaxation time
Probability per attempt
Rate of dissociation
Challenge Problem for the Brave
How much are atoms shaking at room temperature?
Lets take the case of a water molecule.
H
H
O
“Spring constant” between Oxygen and Hydrogen ~ 500 N/m.
k = 500 N/m
Espring = ½ k x2
Each degree of freedom has ½ kBT energy (on average)
?Give answer as % of bond length
kB = 1.38 × 10-23 m2 kg s-2 K-1