What is an important factor in SCM phase transitions?
the dynamics of the transition
What are the most common transition types?
- liquid liquid
- melting and crystallisation
What is used to predict phase coexistence?
mean field theory
How are liquid-liquid transitions described?
- quantum behaviour is not important
- use mean field theory to calculate free energy of mixing
- assume no concentration fluctuations
Entropy of liquid-liquid mixing
- 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
Energy of liquid liquid mixing
- 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
When is a system spinodal?
- when the curve of free energy is zero
- beyond this the system is unstable to small composition fluctuations
When is a system metastable?
- when fluctuations in composition increase the free energy
- to achieve phase separation the system must go through an energy barrier
When is a system unstable?
- when fluctuations in composition reduce the free energy of the system
- the system phase separates
What liquid demixing mechanism occurs below the spinodal curve?
- unstable composition
- phase separation occurs by continual composition change
- results in an irregular structure
What liquid demixing mechanism occurs in the metastable region?
- nucleation of one phase into the other
- often involves an activation energy
Why is the mixture unstable within the spinodal curve?
- all composition changes reduce the free energy
- fluctuations are amplified
What does the strange free energy curvature cause?
- flow of matter from areas of low concentration to areas of high concentration
- fast diffusion has a higher energy cost
How are droplets formed?
by large fluctuation in mole fraction
- small droplets formed
How is the decomposition process characterised?
- by a length scale
- optimum size of droplets formed fastest
- forms patterns in the decomposition process
How do domain sizes change?
- 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
Why is classical nucleation theory needed?
- 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
How are freezing and melting described?
- 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
How are heterogenous and homogenous nucleation different?
- homogeneous nucleation which occurs in pure solution
- heterogeneous nucleation which involves a 3rd species in addition to the melt solid
Describe Homogenous Nucleation
• 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,
How does a crystal form in homogenous nucleation?
- 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
Describe Heterogenous nucleation
- 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
