1. Chemistry and Physics of Hybrid Organic-Inorganic Materials
Lecture 3: Material Interactions in Hybrids
Todays lecture will provide background information on the nature of bonding and non-bonding interactions and how they contribute to material properties. Introduce you to some very basic sol-gel hydrolysis and condensation chemistry involved in making the inorganic part of these hybrids. And talk some about the themodynamics of phase separation-both of particles and later of emulsions and polymers.

2. Material Interactions in Hybrids
Non-bonding interactions
Bonding interactions
Surface tension
Free energy
Changes of phase
Phase separation
Crystalline or amorphous

3. Length Scales

4. Proteins – one of the organic phases from Biohybrid Org-Inorganics
Interactions between atoms within the protein chain
Interactions between the protein and the solvent

5. Bonding (& non-bonding)interactions
London forces < 1 kJ/mole
Dipole-dipole 10 kJ/mole
Hydrogen Bonding kJ/mole
Charge-charge
interactions kJ/mole
Covalent bonds kJ/mole
There are a whole bunch of weak non-bonding forces like London and dipole-dipole. They are all weaker than hydrogen bonds, but can add up and be important when surface areas between phases are really large (think bugs crawling on ceiling). Ionic interactions are not the same as the strong ionic bonds in NaCl. These are longer range interactions between fewer groups. None of the non-bonding interactions compare to covalent bonds (or metal or ionic bonds-not ionic interactions). Covalent bonds are strong. So why are materials so weak? We will discuss how to calculate theoretical material strength based on bond strength later
1 kJ mol-1 = 0.4 kT per molecule at 300 K

6. Van der Waals (Non-bonding) Interactions
Nonspecific forces between like or unlike atoms
Decrease with r6
approximately 1 kJ/mol
If r0 is the sum of van der Waals radii for the two atoms. Van der Waals forces are attractive forces when r> r0 and repulsive when r< r0.
~ to J, corresponding to about 0.2 to 2 kT at room
From 3SCMP

7. Charge-charge (Coulombic) interactions
= 10-18J
Coulomb interaction between two ions (1-15 A)
At close range, Coulomb interactions are as strong as covalent bonds (10-18J or kT)
Their energy decreases with 1/r and fall off to less than kT at about 56 nm separation between charges
In practice, charge-charge interactions have been shown to be chemically significant at up to 15 Å in proteins
eo is the permittivity of free space and e is the relative permittivity of the medium between ions (can be vacuum with e = 1 or can be a gas or liquid with e > 1).With Q1 = z1e, where e is the charge on the electron and z1 is an integer value.
The interaction potential is additive in crystals

8. Hydrogen Bonding
In a covalent bond, an electron is shared between two atoms.
Hydrogen possesses only one electron and so it can covalently bond with only ONE other atom.
The proton is unshielded and makes an electropositive end to the bond: ionic character.
Bond energies are usually stronger than v.d.W., typically kT.
H-bonding can lead to weak ordering in water.
From 3SCMP

9. 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 Jm2)
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)
It costs energy to phase separate and make an interface
Small particles have higher surface area per gram; higher energy

10. surface area versus diameter for particles

11. Same polymer volume before and after coalescence:
Particle Coalescence
Same polymer volume before and after coalescence:
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.
From 3SCMP

12. Covalent Bond Dissociation Energies
Si-Si 221 kJ/mole Si-C 300 kJ/mole C-C 350 kJ/mole C-O 375 kJ/mole C-H 415 kJ/mole Al-O 480 kJ/mole Si-O 531 kJ/mole Ti-O 675 kJ/mole Zr-O 750 kJ/mole
Two electrons per bonding molecular orbital
BDE = potential energy, -dU
Force (N or kgms-2)
to break a bond = -dU/dr
Strength of a bond (Nm-2 or Pa)
= Force/cross section area
Now on to bonding interactions. These are a select list of covalent bond energies. Remember diamond is the worlds highest melting material (3550 °C). Yet its bonds are only half as strong as zirconium-oxygen bonds. That’s because, diamonds have fewer defects are are closer to their theoretical material strength that’s directly derived from the bond strength. Zr-O has more defects in structure.

13. Polymers are weaker than predicted
Linear Macromolecules under tension
causes polymers to disentangle
Polymers typically have tensile strengths of MPa. Tensile strength means to take a piece of plastic and pull it into two pieces. So, these macromolecules are full of C-C bonds, yet their strength is at least 2000X lower than the 200 GPa we calculated. Why? Because the plastic is composed of macromolecules that are interconnected by non-bonding interactions, not covalent bonds. This is the weak link that makes them much weaker than diamond. Some more material strengths are on the next page.
• Entanglements & non-bonding interactions in linear polymers
• Covalent bonds only break with short time scale
• Cross-linking with covalent bonds makes materials stronger but more brittle

14. Thermodynamics of Mixing and phase separation
Entropically mixing is usually favorable (+)
Enternal energy ΔU often is crucial component
Important for mixing of organic and inorganic precursors to hybrids and for phase separation that might occur upon environmental changes or changes in chemical structure

15. Thermodynamics of mixing of mixing A & B
Helmholtz Free Energy (Constant Volume)
For small molecules, NA = NB = 1 & ΔS is large and positive.
ΔS polymer < ΔS molecule
Re-write in terms of an interaction parameter Chi time kT times the volume fractions of A and B
Now you can just vary Chi and T and explore phase diagrams

19. Spinoidal decompositon into two phases
When moving from the one-phase to the two-phase region of the phase diagram, ALL concentration fluctuations are stable.
The two phases have a characteristic size scale defined by a compromise.
If the sizes of the phases are too small: energy cost of extra interfaces is too high.
If the phases are quite large, it takes too long for the molecules to travel the distances required for phase separation.

20. Spinodal decomposition of mixture of liquid crystals

21. A schematic illustrating a typical time evolution of domain formation during spinodal decomposition. With a progress of the decomposition, a sharp interface between two phases develops to form a periodic bicontinuous structure (process I). After the relatively early stage, the bicontinuous structure starts to coarsen to reduce the interfacial area (process II). The coarsening occurs with dynamical self-similarity (c, d, e); that is, forms of the structures are statistically identical at various times, while the characteristic sizes increase with time. The coarsening process is followed by fragmentation of the minority phase and subsequent restructuring due to minimization of surface energy, which finally results in spherical domains and a continuous matrix (f).
Phases grow in size to reduce their interfacial area in a process called “coarsening”.

22. Block copolymers tie the two immiscible phases together
Still spinodal decomposition
Coarsening is stopped by connected macromolecules
Covalent bonds [provide greater metastability of turing structure

23. Nucleation in metastable regions
Small fluctuations in composition are not stable.
Only f1 and f2* are stable phases! The f2* composition must be nucleated and then it will grow.

24. From G. Strobl, Polymer Physics, Springer
Nucleated structure: islands of one phase in another
Spinodal structure: co-continuous phases
From G. Strobl, Polymer Physics, Springer

25. 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.
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

26. Formation of bonds: Polymerization
Hydrolysis:
Condensation:
Net Polymerization:
Shown here for formation of a silsesquioxane

27. Most hybrids involve phase separation
All nucleation. Rare to see spinodal decomposition

28. Amorphous versus crystalline
Amorphous – kinetic, no long range order, no time for crystals to grow from solution or liquid.
How can you tell if a material is amorphous?
Crytsalline: thermdynamic structures made with reversiblity to remove defects and correct growth. Long range order.
How can you tell if a material is crystalline?

29. Crystalline materials
Long range order: Bragg diffraction of electromagnetic radiation (or electron beams in TEM) by crystalline lattice into sharp peaks.
Solid structures with geometric shapes, straight lines and flat surfaces, and vertices.
Optical affects like bifringence
Direct visuallization of crystal at molecular level with AFM or STEM.
Melting point (not always though)

30. AFM of polyethylene crystallite
microcrystals
Inorganic crystals
XRD from semicrystalline
polymer film
Rutile titania crystals in amorphous TiO2
Micrograph of polymer crystalline spherulites

31. XRD (wide angle)
Single crystal or microcrystalline powder (crystals with atomic or molecular scale order)

32. X-ray powder diffraction from polybenzylsilsesquioxane “LADDER” Polymer
Big picture is amorphous material.
Small sharp peaks are due to contaminant from preparation
Not a ladder polymer!!!!!!!!!

33. Amorphous materials
No long range order: diffuse peaks may be present, due to average heavy atom distances.
No crystalline geometries, glass like fractures (conchoidal)
Aggregate spherical particles common
Negative evidence for crystal at molecular level with AFM or STEM.
No Melting point

34. XRD amorphous material
Al2O3 thin films prepared by spray pyrolysis
J. Phys.: Condens. Matter 13 No 50 (17 December 2001) L955-L959

35. 2012 EPL

36. Amorphous materials: XRD
crystalline

37. Conchoidal Fractures in amorphous materials
Crystals break along miller planes
Unless microcrystalline

38. If crystals are small compared to impact, conchoidal fracture can occur
In sandstone 3 meters tall)
In metal

39. Summary: Physics of Hybrids
Bonds & non-bonding forces that hold materials together
Surface tension and surface free energy
Thermodynamics of Mixing and phase separation ( of polymers in particular)
Nucleation and Spinodal decomposition
Blends of immiscible polymers and immiscible block copolymers
Nucleation of particles & sol-gel chemistry
Difference between crystalline and amorphous