Workshop 1

Question 1

Define the degree of crystallinity (Dc) and glass transition temperature (Tg) of a polymer. Explain why polyethylene and polypropylene can potentially have high degrees of crystallinity but poly(ethylene-stat-propylene) has almost zero crystallinity.

Answer 1

• The degree of crystallinity measures the volume or weight percentage of the material that forms a periodic regular structure. Due to the long-chain molecules, a polymer cannot fully crystallise.
• Glass transition temperature is a characteristic temperature at which polymers behaviour changes between rigid glassy solid and rubbery material. The spatial arrangement of atoms can change by rotation around the chain. This molecular motion is not possible when the temperature is below Tg due to insufficient internal energy in the material. (amorphous molecules only).

The ability of crystallisation requires a polymer to possess certain stereo-regularity in its molecular structure. A linear long-chain with periodic order allows molecules to be packed in a regular structure leading to high degree of crystallinity. However randomly arranged chains with no stereo-regularity will have a low degree of crystallinity.

Question 2

Find the molar mass of:

poly(vinyl acetate) (C4H6O2)n
poly(vinyl alcohol) (C2H4O) n

Answer 2

PVC is a repeat unit in a polymer chain consists of C4H6O2 having a molar mass of 124+16+16*2 = 86 g/mol

After hydrolysis of PVC, it becomes PVA, whose polymer chains composed of repeat unit of C4H6O with molar mass of 122+14+16*1 = 44 g/mol

Question 3

Calculating the number-average molecular weight if you know Dp?

Answer 3

Mn = Dp*M

M = molar mass
Dp = degree of polymerisation
Mn = number-average molecular weight

Question 4

Define the averaged molar mass formula

Answer 4

Mn = n*M/n = W/n

Question 5

Explain the schematic graph using the Boltzmann superposition principle

Answer 5

The Boltzmann Superposition Principle states that the total strain at time t, is the sum of independent strain responses to any change of stresses over the period time of t. Between t=0 and t=10 hours, the stress caused by 200 N acts along and dictates the total strain. At t=10 hours, the additional stress caused by 100 N starts to act. The BSP treats those two stress changes independently and states the total strain at t >10 hours is the sum of the strain caused by each stress change over the period of time = t

Question 6

Suppose a polymer can be described by Maxwell model, what is the strain formula you would use?

Answer 6

strain[t] = stress[o]/E * (stress[o] /n)*t

Question 7

The viscoelastic behaviour of a certain polymeric material can be described by the standard linear solid model with parameters E1, E2 and n. Write down the creep compliance J(t) of a material as a function of time.

Answer 7

strain[t] = stress[o]/E2 * [ 1 - exp (-t/tow)]

tow = n * (1/E1 + 1/E2)

Question 8

Explain why the materials used to reinforce polymers are produced in the form of thin fibres

Answer 8

1. A lower probability of a large flaw being present (size effect) maximises the fibre strength.
2. Small diameters provide large surface area for bonding the fibre with the matrix.
3. Small diameters provide sufficient flexibility in fibre production