Write short notes on crystallinity, number average molecular weight and fatigue of polymers.

1. Crystallinity

Polymers have crystalline regions, where chains are packed in an ordered, regular way (crystallites or lamellae formed by folded chains), and amorphous regions, where chains are randomly coiled and tangled. Most polymers are semi-crystalline. Degree of crystallinity = (mass of crystalline part / total mass) × 100.

• Crystallinity is favoured by linear, regular (isotactic or syndiotactic) chains, small or no side groups, and strong intermolecular forces. Examples: HDPE, nylon, isotactic PP.
• Highly crystalline polymers have higher density, strength, hardness, T_m and chemical resistance, but they are less transparent and more brittle.
• Amorphous polymers (PS, PMMA, atactic PVC) are transparent and show only T_g.

2. Number-average molecular weight (M̄_n)

A polymer is a mixture of chains of different lengths, so its molecular weight is an average. M̄_n is the total weight of all molecules divided by the total number of molecules:

\( \bar M_n = \dfrac{\sum N_iM_i}{\sum N_i} \)

Here N_i is the number of molecules of molecular weight M_i. It is determined by colligative-property methods (osmometry, end-group analysis, ebullioscopy). It is sensitive to low-molecular-weight fractions. M̄_w/M̄_n = PDI, which is at least 1.

3. Fatigue

Fatigue is the weakening and eventual failure of a polymer under repeated (cyclic) loading at stress levels well below its tensile strength. Micro-cracks start at defects and grow with each cycle until the part fractures. Hysteresis heating in viscoelastic polymers speeds this up.

• Fatigue strength / endurance limit: the stress below which failure does not occur for a given (large) number of cycles. It is shown on S–N curves.
• It is important for gears, springs, hinges (e.g. PP living hinges), tyres and vibrating parts.