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.

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

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 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 E thermal =1/2 k * Temperature k = Botzmann’s constant (1.38* J/K) E thermal =1/2 kT Average Energy of each degree of freedom in a system. At room Temperature, E thermal = 4* J or eV

Fahrenheit, Celsius, Kelvin Kelvin Celsius Fahrenheit

Kinetic Energy E kinetic =1/2 (mass)*(velocity) 2 E kinetic = 1/2 mv 2 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. E kinetic =E thermal 1/2 mv 2 = 1/2 kT v=(kT/m) 1/2

Thermally induced Kinetic Energy v=(kT/m) 1/2 (appropriate for a free particle) Person 100kg6* m/s Grain of Sand10  g7*10 -8 m/s ( 10nm/s ) 10 micron bead 4* kg 20 microns/s 1 micron bead4* kg 700 micron/s Virus5* kg9 cm/s Oxygen Molec.5* kg270 m/s

Thermal Vibrations: Carbon Nanotube

Bonding r Force between atoms: attractive and repulsive forces F net =F at +F rep When F net =0, the atom is at its equilibrium position F net =F a +F r =0 These forces are a function of position and depend on the type of bonding F rep F at

How does bond energy relate to the rupture force of a bond? Potential Energy x E b =bond energy x xbxb x b =bond width Transition State EbEb 0

How does bond energy relate to the rupture force of a bond? Potential Energy x EbEb x 0 It Depends...

Effects of thermal energy on Bond Strength Potential Energy x EbEb kBTkBT Thermal Energy affects the Dissociation Constant and Bond Strength. Thermal Energy aids the dissociation of a bond. 0

Bond Strength: Boltzman Factor What is the probability that a bond will spontaneously dissociate???? P=e -E b /kT kT at room temperature = meV The rate of dissociation r d  f  e -E b /k B T Attempt frequency Vibrational frequency of bond or inverse relaxation time Probability per attempt Rate of dissociation

Bond Strength: Boltzman Factor P=e -E b /kT k b T at room temperature = eV = 4 * J k b = 1.38 × m 2 kg s -2 K -1 The rate of dissociation r d  f  e -E b /k B T Attempt frequency Vibrational frequency of bond or inverse 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 E spring = ½ k x 2 Each degree of freedom has ½ k B T energy (on average) ? Give answer as % of bond length k B = 1.38 × m 2 kg s -2 K -1