Bonding

There are four main types of bonds, split into two groups. The strong primary bonds (Ionic, macromolecular covalent & metallic), and the weaker secondary bonds (molecular covalent and van der Waals):

Ionic

• This is the electrostatic force of attraction between oppositely charged ions

• It is formed by electron transfer: metal lose electrons while non-metals gain them

• It is non-directional

• High melting/boiling points

• Easily soluble

• Poor conductivity when solid, but when molten, charged ions are free to move around

• Generally crystalline solids at room temperature & pressure

Covalent

• This is formed from a shared pair of electrons

• Typically occurs if an atom’s outer shell is about half empty (gaining/losing ~four electrons requires too much energy)

• It is directional: the formation and orientation affects the overall molecular shape

There are two types:

Molecular Bonds (simple covalent):

• These have a low melting and boiling point, due to the weak intermolecular forces

• They have poor solubility in water

• Conductivity is also poor, as there are no ions, and all electrons are fixed

• Generally gaseous or liquidous at room temperature and pressure

Macromolecular Bonds (giant covalent):

• These have very high melting and boiling points, as the bonds themselves are very strong and there are very many of them, so a vast amount of energy is required to break these

• Insoluble in water

• Mostly do not conduct, but graphite does

• Generally solid at room temperature and pressure

Metallic

• This is the electrostatic force between positive metal ions (cations) and a sea of delocalised electrons (which are negatively charged)

• The cations are in regular rows, with the electrons free to move (hence conduct) around them

• Melting/boiling points are high, as there are strong electrostatic forces between cations and electrons

• Insoluble in water

• Very good conduction

• Generally shiny, malleable solid at room temperature and pressure

Van der Waals

• Dipoles form when an atom has a net charge, due to an imbalance in protons and electrons

• Dipoles can be temporary or permanent

• Once a dipole forms, it encourages the neighbouring atom to become an oppositely charged dipole

• This +/- force of attraction is the van der Waals bond

A hydrogen bond is a particular type of van der Waals bond. Since the hydrogen atom is the smallest (with just 1 electron in one shell), when it combines with much larger atoms such as nitrogen, oxygen and fluorine, there is a major electromagnetic imbalance. This causes permanent dipoles to form. These give rise to far stronger bonds than temporary dipoles.

• A common example is water. It is the hydrogen bonds that cause a solvent to be polar.

As you can see from the tetrahedron above, most materials have predominantly one type of bond throughout their structure, but some (like ceramics and polymers) have a mixture.

Polymers typically consist of long chains of carbon atoms that are covalently bonded with other atoms (hydrogen, boron etc). These bonds are extremely strong and rigid, with deformation only occurring in extreme conditions.

It is the weaker van der Waals bonds that also exist between molecules in polymers that make them flexible and easy to break.

Interatomic Forces & Bond Energies

When two oppositely charged atoms (or ions) are far apart, their attraction is negligible. As they get closer, however, the attractive force between them increases.

Yet at a certain point, the atoms get so close that the electron clouds start to overlap. At this point, the negatively charged electrons repel each other, causing a repulsive force, between the oppositely charged atoms.

The repulsive force only acts at a very short range

The net force between the atoms, F, will therefore be given by:

The potential energy in the bond is calculated as the integral of the resultant force with respect to separation:

There is a certain separation, r₀, where the resultant force is equal to zero and the bond energy is at a minimum

Potential energy of a bond is often also defined using power laws. A common example is:

• The first term is from the attractive force, the second from the repulsive force

• A, B, m & n are system constants

Typical values for m and n are:

• m = 1 for ionic bonds

• m = 2, n = 9 for covalent bonds

• 1 ≤ m ≤ 4 for metallic bonds

Differentiating this gives an expression for the force:

This equation can be used to determine the equilibrium spacing, by setting F to equal zero.

Potential Energy – Interatomic Separation Graphs

At the equilibrium:

• the atoms are a distance of r₀ apart

• the force is zero

• the energy is at a minimum: E₀

As r < r₀, there is an immense amount of energy in the strongly repulsive bond.

When r > r₀, there is never a positive energy (it tends to zero)

Interatomic Force – Separation Graphs

These are the exact opposite of the energy graph.

Finding Metallic Young’s Modulus

We can approximate the Young’s Modulus for metals very accurately from the force in the metallic bonds:

Young’s Modulus, E, is directly proportional to the gradient of the straight-line segment immediately after r₀:

This does not apply to non-metals, as their structure is fundamentally different.

This must not be used to estimate UTS, as it will give a far higher value:

• Predictions of UTS using this method will be in the range of E/10 or E/15

• The actual UTS of metals is more like E/100 or E/1000

Thermal Expansion

We can use the energy-separation graph to explain thermal expansion:

• r₀ is given as the midpoint on the horizontal line connecting the two points on the curve that have the same energy

• As the temperature increases, so does the energy in the system

• Therefore, the horizontal line connecting the two points gets longer

• Since the gradient on the right of the minimum point is shallower, the horizontal line grows more on the right than it does on the left

• Therefore, the midpoint, r₀, moves to the right as the energy increases

As the temperature increases, the equilibrium spacing between atoms increases. This is thermal expansion.