# States of Matter

### A407 Special Topic: States & Properties of Matter Modules 1-4

Prof Mahesh Bandi

Description: This is a series of four special topics courses presented over two terms (two courses per term). It treats the standard (gases, liquids, and solids) and a few exotic (polymers and colloids) classical states of matter, and explains how these states and their bulk properties emerge from the few interatomic and intermolecular forces at play. The emphasis is on developing strong physical intuition for microscopic mechanics using the simplest models that illuminate the concept. In doing so, we explain both the strengths and shortcomings of these simple models, and in particular, analyse the limiting conditions where they fail. Therefore, rather than theoretical rigour, the focus of the treatment is on performing quick order-of-magnitude calculations. As a result, although the mathematics is unsophisticated, Calculus is a pre-requisite. Wherever possible, scientific facts will be connected with the seminal experiments that established them.

Textbook or required reading:

There is no prescribed textbook for this course. Lectures will be based on notes developed from diverse sources.

Type of Assessment:

There will be regular assignments that include traditional problem sets and the study and critique of seminal scientific articles. There is no exam for the course. All assessment is based on homework assignments.

**Module 1, Term 2**

Duration: 6 Weeks (Jan-Feb 2019)

Class Meetings: Lab 3, B714a. Wednesday 2pm - 4pm, Thursday 3pm - 5pm.

Syllabus:

1. Atoms, molecules and forces.

- Atoms

- Molecules

- Interatomic & Intermolecular forces

2. Thermodynamics review.

- Temperature

- Heat

- Laws of Thermodynamics

3. Ideal Gases - properties & simple theory.

- Bulk properties

- Elementary kinetic theory of the ideal gas

- Ether theory of the ideal gas

- Transport phenomena

4. Further theory of ideal gases.

- A better kinetic theory

- Sedimentation

- Temperature variation of reaction rates

- Velocity distribution of ideal gas

- Thermal energy of molecules

- Macroscopic examples of Equipartition of energy

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**Module 2, Term 2**

Duration: 6 Weeks (March-April 2019)

Class Meetings: Lab 3, B714a. Wednesday 2pm - 4pm, Thursday 3pm - 5pm.

Syllabus:

1. Real (imperfect) gases.

- Deviations from ideal behaviour

- Kinetic theory of real gas: The van der Waals equation

- Some properties of the critical point

- Law of corresponding states

- Internal energy, specific heat capacity of van der Waals gas

- Expansion of gases

2. The Solid State.

- Types of solids

- Solid-liquid transitions: surface & bulk melting

- Consequences of interatomic forces on solids

- Amorphous solids (glasses)

3. Solids: elastic properties.

- Basic elastic properties

- Propagation of longitudinal waves along an elastic bar

- Bulk moduli

4. Solids: strength.

- Deformation

- Dislocations

- Vacancies, diffusion and creep

- Brittle solids

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**Module 3, Term 3**

Duration: 6 Weeks (May - June, 2019)

Class Meetings: TBD.

Syllabus:

1. Solids: thermal & electrical properties.

- Specific heat capacity

- Thermal expansion: Gruneisen's law

- Thermal conductivity

- Electrical conductivity of metals

2. The liquid state.

- Liquid as a modified gas

- Structure: The radial distribution function

- Liquid as a modified solid

- Latent heat of fusion

- Melting point: The Lindemann model

- Vapor pressure

- Dilute ideal solutions

- Surface tension

- Liquid crystals

3. Liquids: flow properties.

- Ideal liquide: Bernoulli's equation

- Real liquids: Viscosity

- Rigidity of liquids

- Non-Newtonian flows

4. Colloids

- van der Waals forces between macroscopic bodies

- Principles of stabilisation

- Stabilization by diffuse electrically charged double layer

- Stabilization by adsorbed polymers: entropic repulsion

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**Module 4, Term 3**

Duration: 6 Weeks (June - July, 2019)

Class Meetings: TBD.

Syllabus:

1. Polymers

- Conformations.

- Effective size & radius of gyration

- Dilute polymers: chain configurations - Zimm theory

- Molten polymer: Conformations, Viscosity, Diffusion, and effect of shear rate on flow

- Four main states of polymers

- Factors affecting the Glass transition temperature

- Time-temperature superposition: stress relaxation

- The linear viscoelastic model

- Morphology of the glassy state

- Elastic properties of polymers in glassy state

- Yield properties and deformation mechanisms

- Morphological changes in shear and rupture

- Brittle behaviour

- Cross-linker polymers

- Polymer composites

2. Dielectric properties of matter

- Basic dielectric relations

- Polarization of gases

- Polarization of polar molecules

- Optical dispersion and anomalous dispersion

- Dielectric properties of liquids and solids

3. Magnetic properties of matter

- Magnetic equations

- Diamagnetism: Langevin's treatment

- Paramagnetism: Langevin function

- Ferromagnetism

- Quantum treatment of magnetic properties