ForceEnergyEntropy

Free Energy

What is Force ?

F=ma

force mass accel.

What is Force ?

S 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 ? S 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 Fg=mg m

This is a special case. When one of the two objects is Earth

Gravitation

m1

Fg=Gm1m2

r2

m2

r

G = 6.67×10−11 N m2 kg−2

Electrostatic

q1

Fe=ke

q1q2

r2

q2

r

ke=9.0 x 109 Nm2/C2

q is the amount of charge on each object

Charge of an electrone = 1.6 * 10-19 C

C= Coulomb a unit of charge

SarahAshley

ChristianZack P.

CharlieJeremy

DominiqueCarly

TrevorKarsten

JessyZack J.

SamAhmet

John

CoreyAakashHunterCarson

ShaneNickMax

1 2 3

4 5 6

Nanocalc Teams

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?

Potential Energy U (or E)

Potential Energy U (or E)

F

Force, Energyand Bonding

Force, Energyand Bonding

A

B

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 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 motionVery, Very cold

Warm

Hot

Flow of Heat

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

Celsius

Fahrenheit

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 mg 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

Entropy

Entropy

DS < 0

Entropy

Entropy

DS < 0

Entropy

Entropy

DS > 0

Bonding/Assembly

Bond Energy vs. Thermal Energy

Force, Energyand Bonding

Free EnergyEnthalpy and Entropy

Pot

enti

al E

nerg

y

xEb=bond energy

x

Transition State

Ub

0

Uactiv.

x

Bonding / Assembling

x

Disassociating

Pot

enti

al E

nerg

y

xUb

x

0

Bonding / Assembling

Pot

enti

al E

nerg

y

xUb

x

0

Disassociating

Effects of thermal energy on Bond StrengthP

oten

tial

Ene

rgy

xUb

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-Ub/kTkT at room temperature = 0.025 meV

The rate of dissociation

rd = w e-Ub/kBT

Attempt frequencyVibrational frequency of bond orinverse relaxation time

Probability per attempt

Rate of dissociation

Force, Energyand Bonding

Force, Energyand Bonding

A

B

DU = UB –UA < 0Spontaneous & Stable

Gibbs Free Energy

G = - H TS

Thermodynamic Potential

Helmholtz Free Energy

F = U - TS

Temp EntropyEnthalpy

U + PV

Potential Energy (chemical typically)

Thermodynamic Potential

Helmholtz Free Energy

F = U - TSDF = DU - TDS

When change in free energy is negative, process is spontaneous

Define System

DF = DU – TDS

DU = ? > or < 0 ?DS = ? > or < 0 ?

When change in free energy is negative, process is spontaneous

Bond Strength: Boltzman FactorWhat is the probability that a bond will spontaneously dissociate????

P=e-Ub/kTkT at room temperature = 0.025 meV

The rate of dissociation

rd = w e-Ub/kBT

Attempt frequencyVibrational frequency of bond orinverse relaxation time

Probability per attempt

Rate of dissociation

DU > or < 0 ?DS > or < 0 ? DF = DU - TDS

DU > or < 0 ?DS > or < 0 ? DF = DU - TDS

AB

C

D

EWhich representative state of the fiber has highest entropy?