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Polymers and composites

Learn the types of polymerization, molecular weight and its distribution, crystallinity, the glass transition temperature, viscoelastic models, thermoplastics versus thermosets, and the rule of mixtures and critical fiber length with multiple-choice questions, with practice calculations and explanations.

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Polymers and composites: key points

Polymers consist of long molecular chains in which monomers are linked by addition or condensation polymerization. Molecular weight has a distribution, and the ratio of the weight-average molecular weight Mw to the number-average molecular weight Mn indicates its breadth. In crystalline polymers, which mix crystalline and amorphous regions, the crystallinity governs density, stiffness and transparency, and the temperature at which molecular motion in the amorphous regions freezes is the glass transition temperature Tg.

Polymer deformation is viscoelastic, depending on time and temperature, and stress relaxation and creep are represented by the Maxwell and Voigt models. The stiffness of fiber-reinforced composites is estimated by the isostrain rule of mixtures along the fibers and the isostress rule perpendicular to them, and for short fibers the critical fiber length determines the reinforcing effect.

All Polymers and composites questions (12)
  1. Which polymer is synthesized by condensation (step-growth) polymerization?
  2. Which is a characteristic of thermosetting resins?
  3. Which statement about the glass transition temperature Tg and melting point Tm of a crystalline (semicrystalline) polymer is correct?
  4. A polymer sample consists of equal masses of molecules with a molecular weight of 1.0×10⁴ g/mol and molecules of 1.0×10⁵ g/mol. Which correctly gives the number-average molecular weight Mn and the weight-average molecular weight Mw?
  5. Take the density of perfectly crystalline polyethylene as 1.000 g/cm³ and that of fully amorphous polyethylene as 0.850 g/cm³. Which value is closest to the crystallinity (mass fraction) of a sample with a density of 0.925 g/cm³?
  6. For the same type of polymer, what generally happens as the crystallinity increases?
  7. When a plasticizer is added to poly(vinyl chloride) (PVC), what happens to the glass transition temperature Tg and the properties of the material?
  8. Which statement about mechanical models of viscoelasticity is correct?
  9. A constant strain is applied to a polymer that can be represented by the Maxwell model, and the initial stress is 5.0 MPa. If the relaxation time is 50 s, which value is closest to the stress after 100 s?
  10. A composite contains carbon fibers (Young's modulus 230 GPa) aligned in one direction in an epoxy resin (Young's modulus 3.5 GPa) at a volume fraction of 60%. Using the rule of mixtures, which value is closest to the Young's modulus in the fiber direction?
  11. Which correctly describes the idea of time–temperature superposition in polymer viscoelasticity?
  12. A composite consists of carbon fibers with a diameter of 7.0 µm and a tensile strength of 3.5 GPa in a resin whose fiber–matrix interfacial shear strength is 50 MPa. Which value is closest to the critical fiber length lc = σf·d/(2τc) needed to make full use of the fiber strength?

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