1. Physics and Chemistry of Hybrid Organic-Inorganic Materials Lecture 4: The physics of phase separation and solutions
Professor Douglas A. Loy
Visiting from the University of Arizona, United States

2. Key points for phase separation and solutions
Phase separation is thermodynamic
Phase separation is a part of most hybrids formation
Sol-gel systems form supersaturated solutions that phase separate solid particles (nucleation control).
Sol-gel polymerization of hybrid monomers leads can lead to single solid phases, but there is often a liquid or gas phase created by particle percolation and gelation.
Hybrid based on organic polymers undergo enthalpically driven phase separations
There are nucleation and thermodynamic (spinoidal) controlled phase separations.
Particles form by nucleation phase separation
Surfactant templating is the formation of a material in one phase of a phase separated surfactant-solvent system

3. Phase separation in Hybrid systems
Phase separation occurs frequently in the formation and processing of hybrid organic-inorganic materials
You must be able to recognize how many phases are present in order to characterize and understand a hybrid material.
It is not always as easy as with oil and water to tell how many phases are present

4. Hybrid Organic-Inorganic Thermodynamics of Mixing/Phase separation
phase separation and mixing are opposite thermodynamic processes
We will describe the thermodynamics of these processes with Helmhotz free energy, ΔF
For either:
ΔF < 0 means phase change is favorable
ΔF > 0 means the existing state is more stable and no change.
ΔF = ΔU –TΔS

5. Thermodynamics of single component phase changes
This is just the free energy diagram for a solid melting into a liquid. Below the melt point the solid phase is more stable and above the melt point the liquid is more stable (lower in free energy).

6. Thermodynamics of single component phase changes
Same as before.

7. Thermodynamics of mixing: Two phases going to become one
Dissolution
Inorganic F
organic
2 phases
In this case, the change Helmhotz free energy:
ΔF (mixing) = ΔU –TΔS < 0
One phase: a solution
In a two phase system dissolution or making a solution is thermodyanmically favorable when the change in free energy is negative. This means that the solution is downhill or has a lower free energy than the inorganic and organic phases being mixed. This is not making a mixture. The inorganic phase must actually dissolve in the organic, not just float around.
Thermodynamically favorable mixing of two phases into one
ΔS is generally positive for mixing & gets larger with temperature
ΔU is often positive (unfavorable) with mixing polymers.
Rare, but this could occur with an inorganic monomer dissolving in a polymer

8. Thermodynamics of phase separation: One phase unable to separate into two
Inorganic
In this case, the change Helmhotz free energy:
organic
2 phases F
ΔF(phase separation) = ΔU –TΔS > 0
Thermodynamically unfavorable phase separation: “uphill”
The kT at this time is insufficient to drive phase separation.
This phase separation is the reverse of the dissolution shown on the previous slide. Our solution cannot return to having its organic and inorganic constituents as separate phases because the energy cost is too great.
One phase: a solution
Hybrids with organic and inorganic components bonded together at the monomer level are unable to phase separate

9. Thermodynamics of mixing: Two phases not changing
Inorganic
organic
Inorganic
organic
2 phases
Insoluble
still two phases
ΔF(mixing) = ΔU –TΔS > 0
This slide represents physically mixing an inorganic phase and an organic phase to make a mixture that has two phases. The inorganic cannot dissolve because the thermodynamics are not favorable. You have to be careful, some cases appear to be insoluble, but really are soluble with really slow dissolution rates.
Either temperature is not high enough to dissolve the particles
and/or
the ΔU (internal energy; like enthalpy) is too positive for the entropy to overcome
This is what happens with mixing inorganic particles and organic polymer.

10. An example of a hybrid composed of inorganic (silica) particles mixed in with a fluorinated polymer electrolyte (Nafion)
Two solid
immiscible
phases
Must be physically mixed
As it says.
5 weight percent ex situ silica in Nafion

11. Thermodynamics of mixing: one phase separating into two
One phase: a solution F
2 phases
ΔF (Phase separation)
= ΔU –TΔS < 0
This is the case where a single phase hybrid spontaneously phase separates into an inorganic phase and an organic phase. This generally happens when the temperature is reduced or one or both of the two phases is growing due to polymerization chemistries.
Thermodynamically favorable phase separation of one phase into two phases: This is how particles form in sol-gel and what can happen when a monomer dissolved in another polymer polymerizes.
Inorganic
organic

12. Phase separation of particles from an inorganic monomer dissolved in a viscous polymer solution
The silica monomer forms oligomers and polymers that eventually nucleate out as spherical particles
An example of silica in Nafion membranes made by the process described on the previous slide.
In situ Silica particles

13. Phase diagram of a hybrid organic inorganic material
Two phases at lower temperatures
One phase at higher temperatures
Maximum insolubility is when there are nearly equal quantities in the mixture.
Phase diagrams are an important tool in studying multi-phase materials. This phase diagram shows the two phases inside the arch (binodal line) and the solution of the two that forms at higher temperatures or when one or the other of the phases is in excess.

14. Phase diagram of a hybrid organic inorganic material: Effect Molecular weight on phase separation
With increasing molecular weight of one or both of the solutes, the phase boundary (binodal line) increases in temperature
As Mw increases entropy change becomes less positive.
Hybrids often experience phase separation
When molecule weight increases, many molecules are being attached to each other. This reduces the entropy of the system making the macromolecule less soluble. This characteristic is widely used to purify polymers of any residual monomers that will stay in solution when the polymer is precipitated out with the addition of a non-solvent for the polymer.
Bold line – highest molecular weight
Dashed line –lowest molecular weight

15. More information from phase diagrams: Plots of ΔF at different temperatures
stable
(a)
(b)
(b)
(c)
(d)
(c)
unstable
The Phase diagram is essentially the top view of a number of free energy versus composition plots stacked together.
(d)

16. Overlaying the plots of ΔF on the original phase diagram reveals a metastable region
spinodal line
spinodal lines
stable
(a)
(b)
organic rich phase
composition
Inorganic rich phase
composition
(c)
This slide shows how we translate from one graph type to the other. The spinodal lines comes from the observation that the free energy versus temperature plot looked like a vertebrae. The spinodal lines are at the inflection point. Between the lines the unstable phase can decompose productively with essentially no barrier. Between the spinodal and binodal lines, there is an activation barrier to phase separation. See latter slides.
(d)
spinodal lines
unstable
binodal line
binodal line
metastable
metastable
red = spinodal line
blue - binodal

17. Two phase separation processes:
Spinodal decomposition:
spontaneous.
Fingerprint like patterns.
Between spinodal lines
Nucleation-
not spontaneous, requires nucleation
spherical particles-surface energy important
nucleation kinetics important
spinodal
nucleation
Each phase separation is a easily recognized characteristic that provide clues as to what happened with your material. They also have dramatically different properties.
nucleation
red = spinodal line
blue - binodal

18. Spinodal phase separated materials
red = spinodal line
blue - binodal
When you characterize materials and see this kind of morphology, you know you have a spinodal phase separation.
nucleation
spinodal
nucleation
Freeze fracture TEM
Block copolymers

19. Nucleation phase separated materials
red = spinodal line
blue - binodal
Freeze fracture TEM’s
When you characterize materials and see this kind of morphology, you know you have a nucleated phase separation.
nucleation
spinodal
nucleation
•Spinodal decomposition is mostly about bulk ΔF
•Nucleation also has to account for the instability of the particles due to their small size.

20. Thermodynamics of silica particles forming in sol-gel by nucleation
• Common monomer for silica is Si(OEt)4
• Reactions with water
• Alcohol is solvent because monomer & water are immiscible
• In solution, the monomer hydrolyzes to Si(OH)4 & then polymerizes
•Volume percent silica is in nucleation zone.
• Phase separates as particles only when 1-2 nm in diameter.
Why do the particles grow this big before separating from the solution?

21. Surface tension & the importance of interfaces
Molecules on surface have fewer neighbors and so exert greater force on adjacent molecules = surface tension (in dynes cm-1 or N m-1 Jm-2)
Surface tension γ = surface energy (N m-1 = Jm-2)
Nature tries to minimize the surface area of interfaces (spheres and the bigger the better)
Any interface costs energy to maintain because the molecules on each side have better internal energy relationships with their own kind than with the molecules or atoms in the other phase.
It costs energy to phase separate and make an interface

22. surface area versus diameter for particles
Surface area of spheres goes exponential as the diameter gets below 1000 nm. This helps to account for a lot of the weird behavior of materials made with small particles.
Small particles have higher surface area per gram; higher energy

23. Nucleation of a Second Phase in the Metastable Region
Small: usually a few nanometers
Growth of the second phase occurs only when a stable nucleus with radius r has been formed.
γ is the interfacial energy between the two phases.
Free energy of nucleation. Nucleation is the point at which the particle goes from being in solution to being a separate phase.
Energy reduction through phase separation with growth of the nucleus with volume (4/3)πr3
Energy “cost” of creating a new interface with an area of 4πr2

24. Nucleation free energy plot: critical nuclei size
This is a plot of the interfacial energy which is unfavorable and dependent on the surface area of the particle. The bulk free energy driving force for phase separation is multiplied by the spherical geometry correction. Since the surface area increases slower than volume, the bulk free energy wins out in the end. When the free energy change for nucleation maxes out and starts to decrease that is the point that particles start to persist rather than dissolve. Before that point, any particles will immediately be dissolved.

25. Surface energy/size driving force for particle Coalescence
Same polymer volume before and after coalescence:
In addition to affecting the critical size of nuclei, the surface energy will also drive particles to coarsen (grow or coalesce) or aggregate together. The strong van der Waals attractive forces possible with small relatively smooth particles making aggregation hard to reverse. This means that it is hard to make particles smaller than 100 nm by physical methods because they keep sticking back together. To do so requires a kinetic stablizer.
In 1 L of latex (50% solids), with a particle diameter of 200 nm, N is ~ 1017 particles. Then ΔA = -1.3 x 104 m2
With ϒ = 3 x 10-2 J m-2, ΔF = J.

26. Hybrid systems: small inorganic particles in an organic polymer
You can see the particles that have aggregated together in this Nafion-silica composite membrane in order to minimize their surface energy.
Particles will aggregate into clusters to reduce surface area and lower free energy

27. Other hybrid monomer can undergo a variety of different phase separations
Gel
Silsesquioxanes, a common hybrid organic-inorganic, will phase separate out as viscous liquids from the ethanol solution or as crystals or as particles. Which happens depends on the organic group on the monomer, monomer concentration, solvent, catalyst and other variables. When these particles aggregate into a percolating network, the solvent or air (after drying) in pores are second phases.
No Gel
No Gel
• Must have solid and liquid phase
• Solid phase (usually particles) must be continuous through liquid (percolation)
• Phase separation of liquid prevents further reaction and gelation

28. Now, lets look at a two phase system that stays 2 phases with mixing (emulsions)
Two immiscible liquids
minimizing surface area
Two immiscible liquids forced into very high surface area interface
Meta-stable because of surfactant
This is a liquid liquid two phase system. On the left the oil and water phases have segregated back and have the minimum surface area interface possible. Physically mix the oil and water together and you get the emulsion on the right. It is called an oil in water emulsion simply because there is more water to start with so it gets to be the continuous phase. Without a surfactant, the emulsion will break down and the oil and water layers will reform. This process is fast because the viscous is too low to create a barrier. Surfactants raise the barrier and kinetically stabilize the emulsion.
Two phases
With time
Two phases
The free energy of mixing the oil and water into a (single phase) solution is very, very, very unfavorable (positive)

29. Templating with triblock copolymer is formally a Class 1B material
Polymer is template. After removal, silica remains
The block copolymers used to template silica, silsesquioxane or metal oxide growth are basically a Class 1B system. They are lumped in class 2 in this course, but in the future I will probably move them to this lecture. The triblock above has hydrophilic and hydrophobic phases. Unhydrolyzed monoemr will dissovle in the hydrophobic phase but as it hydrolyzes, it becomes hydrophilic enough that it migrates into the hydrophilic phase where it condenses into an amorphous structure tempalted by the 3-D structure of the surfactant. Note if you start with the metal salt hydrates they will go into and stay in the hydrophilic phase. We will talk more about these templated materials in the lectures to come, because they are the closet akin to biohybrids that we have to date.

30. Summation Phase separation is an important part of how hybrids form
Many hybrids have multiple phases
Some start as mixtures and end as multiphase mixtures.
Hybrid monomers will form single phase bulk materials, but will form porous materials where air or solvent is a second phase.
The phase separations lead to recognizable structures and morphology that can tell the researcher how to manipulate the hybrids productively.