PHY1039

Properties of Matter

6 February, 2012

Lecture 1

Why Study Matter? Understanding Gases

http://www.jamie.aarontastic.com/Low%20Pressure%20Example.JPG

Meteorology: high and low pressure

Measuring Lung Capacity

http://www.heart-watch-blog.com/images/blogs/7-2007/lung-

capacity-7810.jpg

Ideal Gas:

Pressure, Volume,

Temperature

relationships

http://www.teslasociety.com/mars2.htm

Atmospheres of Planets

Thermal expansion of girders was

restricted by frictional forces. They could

not expand lengthwise, so they buckled!

Joints in bridges are used to

enable thermal expansion.

Why Study the Properties of Matter? Thermal Expansion

Pressure, volume and temperature are interrelated in solids.

http://communication.howstuffworks.com/laptop.htm/printable

Why Study the Properties of Matter? Heat Dissipation

Heat sinks, heat spreaders, and fans remove heat from the CPU of a laptop computer.

(The objective is to do electrical work, but heat is also given off in the process.)

Double-walled Multi-walled Single-walled

Carbon Nanotubes

Why Study the Properties of Matter?

Underlies (Nano)Technology

Electron microscope image of multi-walled carbon nanotubes

S. Iijima, Nature 354 (1991) 56.

Is it possible to construct a lift to satellites orbiting the Earth?

What Happens when Thermal Properties Go Wrong?

A failed O-ring allowed the escape of H2 gas. The result was an explosion = sudden release of heat

Challenger Space Shuttle Disaster

http://www.ssqq.com/archive/disasters.htm

Columbia Space Shuttle Disaster

Damage to the wing caused over-heating on re-entry into the atmosphere

Thermodynamics Provides Equations to Describe Properties of Matter

Properties are inter-related:

• Mechanical (elastic modulus and compressibility)

• Thermo-mechanical (expansivity)

• Thermal (heat capacity)

• Flow (viscosity)

A Typical Phase Diagram for the Three States of Matter

Figure from “Understanding Properties of Matter” by M. de Podesta

Solid Liquid: Melting (heat in) Liquid Solid: Freezing (heat out) Liquid Gas: Boiling (heat in) Gas Liquid: Condensation (heat out) Solid Gas: Sublimation (heat in) Gas Solid: Deposition (heat out)

Phase Transitions

Lines represent conditions where two phases co-exist. Three phases co-exist at the triple point.

Importance of Phase Transitions:

Laser Annealing

Laser annealing to create metal nanoparticles

Intense laser beam can melt

metals. The liquid metal flows and

makes small droplets on the

surface.

If the metal liquid is hot enough, it

evaporates into the air where it

forms nm-sized solid particles when

cooled.

Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html

Phase Diagram for Carbon Dioxide

atm = atmospheres (a unit of pressure)

Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html

Phase Diagram for Water

States of Matter Gas • Atoms/molecules randomly distributed

throughout their container. • Have a distribution of mean speeds. • Travel in all directions. • Low density: the mean free path is about

l= 3 nm in air under standard conditions.

Liquids • Atoms/molecules randomly distributed

throughout their container (like gas). • Have a distribution of mean speeds. • Vibrate in all directions. • Density is higher than in a gas. • Separated from gas by a meniscus.

Crystalline Solids • Atoms/molecules arranged on a periodic

array in three dimensions (a lattice) • Vibrate in all directions • Density is usually higher than the liquid’s.

Atoms are in close contact.

Figures from “Understanding Properties of Matter” by M. de Podesta

Mean Free Path of Gas Molecules

Molecules travel a distance of l in between collisions.

Bonds in Solids

In simple cubic packing, each atom has six nearest neighbours.

The bond between two atoms with a mass of m can be modelled as springs, with a spring constant, K, showing simple harmonic motion with a resonant frequency of f0:

When the atoms vibrate and stretch the springs, the potential energy rises. The kinetic energy also oscillates as the velocity changes during the vibrations.

Figures from “Understanding Properties of Matter” by M. de Podesta

𝑓0=1

2𝜋

𝐾

𝑚

“Sea of electrons”: electrons are shared between all atoms, i.e. delocalised

Ionic bonds: Coulombic attraction between cations (+ve) and anions (-ve)

Weak van der Waals’ attraction between individual charge-neutral molecules; No sharing of electrons

Classification of Solids

(2) Ionic (1) Molecular

(4) Metal (3) Covalent

Electrons are shared in bonds between neighbouring atoms Bonds extend in prescribed directions

Figure from “Understanding Properties of Matter” by M. de Podesta

Potential Energy, u, between Ions

For a singly-charged cation (+ve) and an anion (-ve) at a distance of ro, the potential energy is:

u = −𝑒2

4𝜋𝜀𝑜𝑟𝑜

In an ionic solid, there are interactions between ions in three dimensions and at regularly spaced distances.

Figure from “Understanding Properties of Matter” by M. de Podesta

e = charge on the electron: 1.602 x10-19 C

eo = permittivity of free space:

8.854 x10-12 Fm-1

Potential Energy, u, between Neutral Atoms

Averaged over time, electrons are uniformly distributed around an atom’s nucleus.

But at any given instant, the electron charge distribution is non-uniform.

There is an attraction between the oppositely-charged sides of atoms:

Electron distribution at intervals of 10-16 seconds

Potential energy: r

𝑢~−1

𝑟6

Potential Energy for Non-Charged Atoms/Molecules

r

s

r/s r/s

Po

ten

tial

En

erg

y

Potential Energy

varies with the

separation distance, r. There is also kinetic

energy, which is the

energy of motion.

Figure from “Understanding Properties of Matter” by M. de Podesta

~ r -6