Chemistry and Physics of Hybrid Organic-Inorganic Materials

Chemistry and Physics of Hybrid Organic-Inorganic Materials

Lecture 3: Material Interactions in Hybrids

Material Interactions in Hybrids
Non-bonding interactionsBonding interactionsSurface tensionFree energyChanges of phasePhase separationCrystalline or amorphous

Length Scales

Proteins one of the organic phases from Biohybrid Org-Inorganics
Interactions between atoms within the protein chainInteractions between the protein and the solvent

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

Dipole-dipole10 kJ/mole

Hydrogen Bonding20-40 kJ/mole

Charge-charge interactions0-100 kJ/mole

Covalent bonds150-600 kJ/mole
1 kJ mol-1 = 0.4 kT per molecule at 300 K

Nonspecific forces between like or unlike atomsDecrease with r6approximately 1 kJ/molIf 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 in proteins
= 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 = 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 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 A = -1.3 x 104 m2
With = 3 x 10-2 J m-2, F = - 390 J.
From 3SCMP

Covalent Bond Dissociation Energies
Si-Si221 kJ/moleSi-C300 kJ/moleC-C350 kJ/moleC-O375 kJ/moleC-H415 kJ/moleAl-O480 kJ/moleSi-O531 kJ/moleTi-O675 kJ/moleZr-O750 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 U 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 & S is large and positive.

S polymer < S molecule

Spinoidal decompositon into two phases

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
Only f1 and f2* are stable phases! The f2* 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
Growth of the second phase occurs only when a stable nucleus with radius r has been formed.
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 bifringenceDirect 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)

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 commonNegative evidence for crystal at molecular level with AFM or STEM.No Melting point

XRD amorphous material
Al2O3 thin films prepared by spray pyrolysis
J. 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 togetherSurface tension and surface free energyThermodynamics of Mixing and phase separation ( of polymers in particular)Nucleation and Spinodal decompositionBlends of immiscible polymers and immiscible block copolymers Nucleation of particles & sol-gel chemistryDifference between crystalline and amorphous

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.
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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
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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
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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. Thats because, diamonds have fewer defects are are closer to their theoretical material strength thats directly derived from the bond strength. Zr-O has more defects in structure.
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Polymers typically have tensile strengths of 10-100 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.
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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.

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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).
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