Force Energy Entropy Free Energy

What is Force ? F=maF=ma force mass accel.

What is Force ?  F=ma “Sum of the forces on an object is (directions matter) is equal to the mass of that object multiplied by it’s acceleration”

What is Force ?  F=ma “Sum of the forces on an object is (directions matter) is equal to the mass of that object multiplied by it’s acceleration”

Gravitational F g =mg m This is a special case. When one of the two objects is Earth

Gravitation m1 F g =G m1m2m1m2 r2r2 m2 r G = 6.67×10 −11 N m 2 kg −2

Electrostatic q1 F e =k e q1q2q1q2 r2r2 q2 r k e =9.0 x 10 9 Nm 2 /C 2 q is the amount of charge on each object Charge of an electron e = 1.6 * C C= Coulomb a unit of charge

Electrostatics Coulomb’s Law F = k e q 1 q 2 /r 2 k e =9.0 x 10 9 Nm 2 /C 2 e = 1.6 x C Gravity Newton’s Law of Gravitation F =Gm 1 m 2 /r 2 G = 6.673×10 −11 N m 2 kg −2.

Sarah Ashley Christian Zack P. Charlie Jeremy Dominique Carly Trevor Karsten Jessy Zack J. Sam Ahmet John Corey Aakash Hunter Carson Shane Nick Max Nanocalc Teams

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?

Potential Energy U (or E)

F

Force, Energy and Bonding

A B

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 Entropy ?

What is entropy ? A count of the number of equivalent states of a system Equivalent ? States ??

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

Heat is nano-scopic motion Very, Very cold Warm Hot

Flow of Heat

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

Entropy

 S < 0

Entropy

 S < 0

Entropy

 S > 0

Bonding/Assembly Bond Energy vs. Thermal Energy

Force, Energy and Bonding

Free Energy Enthalpy and Entropy

Potential Energy x E b =bond energy x Transition State UbUb 0 U activ.

x Bonding / Assembling

x Disassociating

Potential Energy x UbUb x 0 Bonding / Assembling

Potential Energy x UbUb x 0 Disassociating

Effects of thermal energy on Bond Strength Potential Energy x UbUb 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 -U b /kT kT at room temperature = meV The rate of dissociation r d  e -U b /k B T Attempt frequency Vibrational frequency of bond or inverse relaxation time Probability per attempt Rate of dissociation

Force, Energy and Bonding

A B  U = U B –U A < 0 Spontaneous & Stable

Gibbs Free Energy G  S Thermodynamic Potential Helmholtz Free Energy F  U  S TempEntropy Enthalpy U + PV Potential Energy (chemical typically)

Thermodynamic Potential Helmholtz Free Energy F  U  S  F =  U - T  S When change in free energy is negative, process is spontaneous Define System

 F =  U – T  S  U = ? > or < 0 ?  S = ? > or < 0 ? When change in free energy is negative, process is spontaneous

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

 U > or < 0 ?  S > or < 0 ?  F =  U - T  S

 U > or < 0 ?  S > or < 0 ?  F =  U - T  S

A B C D E Which representative state of the fiber has highest entropy?