Shaky Nano Property #2: All things shake, wiggle, shiver and move all around at the nanoscale

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