Chemistry and Physics of Hybrid Organic-Inorganic Materials

Lecture 3: Material Interactions in Hybrids

Material Interactions in Hybrids

• Non-bonding interactions• Bonding interactions• Surface tension• Free energy• Changes of phase• Phase separation• Crystalline or amorphous

Length Scales

Proteins – one of the organic phases from Biohybrid Org-Inorganics

• Interactions between atoms within the protein chain• Interactions between the protein and the solvent

Bonding (& non-bonding)interactions• London forces < 1 kJ/mole

• Dipole-dipole 10 kJ/mole

• Hydrogen Bonding 20-40 kJ/mole

• Charge-charge interactions 0-100 kJ/mole

• Covalent bonds 150-600 kJ/mole

1 kJ mol-1 = 0.4 kT per molecule at 300 K

rQQ

rwo421=)(

64 rC

rwo )(

=)(

• 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.

Van der Waals (Non-bonding) Interactions

~ 10-21 to 10-20 J, corresponding to about 0.2 to 2 kT at room

From 3SCMP

Charge-charge (Coulombic) interactions

Coulomb interaction between two ions (1-15 A)

At close range, Coulomb interactions are as strong as covalent bonds (10-18J or 200-300 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

w(r)=Q1Q2

4or= 10-18J

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 25-100 kT.

• H-bonding can lead to weak ordering in water.

From 3SCMP

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

surface area versus diameter for particles

Particle CoalescenceSame 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 = - 390 J.From 3SCMP

Covalent Bond Dissociation EnergiesSi-Si 221 kJ/moleSi-C 300 kJ/moleC-C 350 kJ/moleC-O 375 kJ/moleC-H 415 kJ/moleAl-O 480 kJ/moleSi-O 531 kJ/moleTi-O 675 kJ/moleZr-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

Polymers are weaker than predicted

• 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

Linear Macromolecules under tensioncauses polymers to disentangle

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

Thermodynamics of mixing of mixing A & B

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

Helmholtz Free Energy (Constant Volume)

For small molecules, NA = NB = 1 & ΔS is large and positive.

ΔS polymer < ΔS molecule

Spinoidal decompositon into two phasesWhen moving from the one-phase to the two-phase region of the phase diagram, ALL concentration fluctuations are stable.

Spinodal decomposition of mixture of liquid crystals

Phases grow in size to reduce their interfacial area in a process called “coarsening”.

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

Nucleation in metastable regions

Small fluctuations in composition are not stable.

Only1 and 2* are stable phases! The 2* composition must be nucleated and then it will grow.

Nucleated structure: islands of one phase in another

Spinodal structure: co-continuous phases

From G. Strobl, Polymer Physics, Springer

Nucleation of a Second Phase in the Metastable Region

Energy reduction through phase separation with growth of the nucleus with volume (4/3)r3

Energy “cost” of creating a new interface with an area of 4r2

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.

Small: usually a few nanometers

Formation of bonds: Polymerization• Hydrolysis:

• Condensation:

• Net Polymerization:

Shown here for formation of a silsesquioxane

Most hybrids involve phase separation

All nucleation. Rare to see spinodal decomposition

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?

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)

AFM of polyethylene crystallite

Inorganic crystals

XRD from semicrystalline polymer film

microcrystals

Rutile titania crystals in amorphous TiO2

Micrograph of polymer crystalline spherulites

XRD (wide angle)

• Single crystal or microcrystalline powder (crystals with atomic or molecular scale order)

sin2 hkld=

X-ray powder diffraction from polybenzylsilsesquioxane “LADDER” Polymer

Big picture is amorphous material.Small sharp peaks are due to contaminant from preparationNot a ladder polymer!!!!!!!!!

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

XRD amorphous material

Al2O3 thin films prepared by spray pyrolysisJ. Phys.: Condens. Matter 13 No 50 (17 December 2001) L955-L959

2012 EPL 98 46001

Amorphous materials: XRD

amorphous

amorphous

crystalline

Conchoidal Fractures in amorphous materials

Crystals break along miller planesUnless microcrystalline

If crystals are small compared to impact, conchoidal fracture can

occur

In sandstone 3 meters tall) In metal

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