Part 3

Question 1

What is an important factor in SCM phase transitions?

Answer 1

the dynamics of the transition

Question 2

What are the most common transition types?

Answer 2

• liquid liquid

- melting and crystallisation

Question 3

What is used to predict phase coexistence?

Answer 3

mean field theory

Question 4

How are liquid-liquid transitions described?

Answer 4

• quantum behaviour is not important
• use mean field theory to calculate free energy of mixing
• assume no concentration fluctuations

Question 5

Entropy of liquid-liquid mixing

Answer 5

• consider atoms and molecules to be arranged on a lattice
• in mean field theory sites a and b are independent of each other
• P(a next to b) = P(b next to b) providing the concentrations of a and b are equal
• use Boltzmann equation to calculate the entropy of mixing

Question 6

Energy of liquid liquid mixing

Answer 6

• maximum a,b interaction occurs when their mole fractions are 0.5
• an ideal entropy situation is described where ab> aa and bb interactions
• if X> 2 there are two coexisting phases with minimal free energy

Question 7

When is a system spinodal?

Answer 7

• when the curve of free energy is zero

- beyond this the system is unstable to small composition fluctuations

Question 8

When is a system metastable?

Answer 8

• when fluctuations in composition increase the free energy

- to achieve phase separation the system must go through an energy barrier

Question 9

When is a system unstable?

Answer 9

• when fluctuations in composition reduce the free energy of the system
• the system phase separates

Question 10

What liquid demixing mechanism occurs below the spinodal curve?

Answer 10

• unstable composition
• phase separation occurs by continual composition change
• results in an irregular structure

Question 11

What liquid demixing mechanism occurs in the metastable region?

Answer 11

• nucleation of one phase into the other

- often involves an activation energy

Question 12

Why is the mixture unstable within the spinodal curve?

Answer 12

• all composition changes reduce the free energy

- fluctuations are amplified

Question 13

What does the strange free energy curvature cause?

Answer 13

• flow of matter from areas of low concentration to areas of high concentration
• fast diffusion has a higher energy cost

Question 14

How are droplets formed?

Answer 14

by large fluctuation in mole fraction

- small droplets formed

Question 15

How is the decomposition process characterised?

Answer 15

• by a length scale
• optimum size of droplets formed fastest
• forms patterns in the decomposition process

Question 16

How do domain sizes change?

Answer 16

• size of domain changes with time
• as q increases do does domain size
• coarsening occurs when a system grows into large domains to minimise the total interfacial energy

Question 17

Why is classical nucleation theory needed?

Answer 17

• nucleation of a new phase into an existing one often involves an energy barrier and is an activated process
• The more molecules involved lead to higher energy clusters with higher interface energies

Question 18

How are freezing and melting described?

Answer 18

• No simple mean field theory for these transitions
• There is a change in symmetry going from liquid with local order to a solid with global order
• Kinetics is similar to liquid liquid demixing

Question 19

How are heterogenous and homogenous nucleation different?

Answer 19

• homogeneous nucleation which occurs in pure solution

- heterogeneous nucleation which involves a 3rd species in addition to the melt solid

Question 20

Describe Homogenous Nucleation

Answer 20

• An activated process due to the energy cost associated with the increased interfacial area when a crystal is grown

• Requires high activation energy and nucleation often occurs through heterogeneous nucleation
• Tend to form spheres, unless crystals are involved in which case specific faces grow first
• Free energy change depends on the degree of supercooling,

Question 21

How does a crystal form in homogenous nucleation?

Answer 21

• As you move down in temperature the free energy barrier decreases until at some point it can be overcome by thermal fluctuations, causing the formation of a crystal
• As soon as a crystal forms the rest of the molecules have a lattice template and can also from crystal as there is no longer a free energy barrier

Question 22

Describe Heterogenous nucleation

Answer 22

• Activation energy is reduced
• Described using a contact angle model
• The affinity of a solid towards a surface depends on the contact angle, depending on 3 surface tensions
• Critical radius is independent of a solid and liquid affinity of the mould but free energy is very dependent
• If the contact angle is 180o nucleation will happen in bulk solution “drying transition” and is effectively homogeneous in nature
• As you decrease the contact angle the free energy of heterogenous nucleation becomes more favourable/ larger

Free energy is proportional to surface tension, therefore large areas cause large free energies which lead to aggregation