Basic Concepts of Polymers Questions and Answers

Answer: B

The blend is immiscible due to entropic constraints.

The free energy of mixing is \(\Delta G_{m} = \Delta H_{m} - T\Delta S_{m}\). For small molecules the combinatorial entropy of mixing is large and drives mixing, but for long chains it is tiny, because each chain contributes only one translational unit however many segments it has (in the Flory-Huggins expression the entropy terms are divided by the chain lengths). Even a small positive enthalpy of mixing between the similar but not identical PE and PP segments then outweighs it, and the polymers separate. The paper attributes this to the entropic constraint.

Being polyolefins with similar solubility parameters is not enough for high polymers, so both 'miscible' options are wrong.

Answer: A

The relation is E' = \(\sqrt{3}\) E''.

In dynamic mechanical analysis the loss tangent is the ratio of loss to storage modulus, \(\tan\delta = E''/E'\). With \(\delta = 30^{\circ}\):

\[ \begin{aligned} \frac{E''}{E'} &= \tan 30^{\circ} = \frac{1}{\sqrt{3}} \\ E' &= \sqrt{3}E'' \end{aligned} \]

\(E'' = \sqrt{3}E'\) is the case \(\delta = 60^{\circ}\). The two options with a factor 2 use \(\sin\) or \(\cos\) of 30° (0.5 and \(\sqrt{3}/2\)) instead of the tangent.

Answer: C

The match is P-3; Q-1; R-4; S-2.

• Surface resistivity is the resistance across a square of surface, so its unit is the ohm (often written ohm per square).
• Volume resistivity is resistance times area over thickness: ohm-cm.
• The coefficient of thermal expansion is a fractional change per kelvin: K^-1.
• Electrical conductivity is the reciprocal of resistivity: S cm^-1.

The options pairing surface resistivity with ohm-cm or S cm^-1, or the expansion coefficient with S cm^-1, confuse these.

Answer: B

The match is P-3; Q-4; R-2; S-1.

• Polyurethane: the urethane C=O stretch, about 1720 cm^-1.
• Polyethylene: the CH₂ C-H stretch, about 2914 cm^-1.
• Polysulfone: the symmetric O=S=O stretch, about 1150 cm^-1.
• ABS: the nitrile C≡N stretch from acrylonitrile, about 2234 cm^-1.

The options giving polyethylene the 1720 or 1151 band, or the sulfone the 2234 band, mismatch the groups: polyethylene has only C-H and C-C bonds, and only ABS has a nitrile.

Answer: C

The Maxwell model gives E = (S/G) + (S/\(\eta\))t.

The Maxwell model is a spring (modulus G) and a dashpot (viscosity \(\eta\)) in series. Under a constant stress S, both elements carry the full stress and their strains add. The spring stretches at once by S/G, the instantaneous elongation to l; the dashpot flows at a constant rate S/\(\eta\), so after time t it has added (S/\(\eta\))t, the gradual creep:

\[ E = \frac{S}{G} + \frac{S}{\eta}t \]

On unloading only the spring recovers, which is why the wire retracts by the elastic part and keeps the viscous flow. Subtracting the terms, multiplying them or dividing them has no basis: strains of elements in series simply add.

Answer: B

The correct match is P-3; Q-1; R-4; S-2.

• High density polyethylene: a flexible chain with no side groups, so \(T_{g}\) is far below room temperature, around -100 to -80°C (3).
• Poly(vinyl carbazole): the very bulky, rigid carbazole side group stiffens the chain enough to push \(T_{g}\) above 200°C (1).
• PMMA: an amorphous glassy plastic at room temperature, with \(T_{g}\) usually quoted near 100°C, which is the 90 to 100°C band (4).
• Polycarbonate: rigid aromatic rings in the backbone give \(T_{g}\) near 145 to 150°C (2).

The other options misplace these; any option putting HDPE above room temperature, or PMMA above 200°C, can be ruled out at once.

Answer: C

The keyed combination is 1-Polystyrene; 2-Nylon fibers; 3-Polyethylene; 4-Vulcanized rubber.

Curve 1 has the steepest initial slope and ends abruptly at a small elongation with no yield: a hard, brittle glassy polymer. Polystyrene is the brittle material in the list, and it is the only reading that fits curve 1. That alone settles the answer, since only one option labels curve 1 polystyrene.

The rest follows the same pattern of decreasing stiffness. Nylon fibres (2), oriented and partly crystalline, are stiff and strong and yield at the highest stress. Polyethylene (3) yields at a lower stress and then cold-draws, the stress falling and then rising as the neck propagates. Vulcanized rubber (4) has the lowest modulus and the largest elongation.

The other options give curve 1 to nylon, polyethylene or rubber, none of which breaks in that stiff, brittle way at so small an elongation.

Answer: B

Melting is a first order phase transition.

At the melting point the crystalline regions absorb latent heat, and volume, enthalpy and entropy change discontinuously. Discontinuities in the first derivatives of the Gibbs free energy define a first-order transition in Ehrenfest's scheme.

The glass transition, by contrast, shows only a change in slope of volume and enthalpy (a step in heat capacity and expansion coefficient) and is often described as pseudo-second-order. Zeroth and third order do not describe melting.

Answer: D

Die swell is due to elastic recovery.

A polymer melt is viscoelastic. In the die, the chains are stretched and oriented by shear and elongation, storing elastic energy. When the extrudate leaves the die, the constraint is removed and the chains recover part of that deformation, so the extrudate swells to a larger cross-section than the die (the Barus effect).

Purely viscous deformation is not recoverable and would give no swell, plastic deformation is permanent, and although the melt is both viscous and elastic, the swelling itself comes from the elastic recovery.

Answer: C

The correct matching is P-2; Q-3; R-4; S-1.

1. Notched Izod impact strength is the energy absorbed per unit notch width, in J m^-1 (P-2).
2. Flexural strength is a stress, in MPa (Q-3).
3. Dielectric strength is the breakdown voltage per unit thickness, in kV cm^-1 (R-4).
4. Complex viscosity, from oscillatory rheometry, is a viscosity, in Pa s (S-1).

The other options give impact strength the unit of viscosity or stress, or swap the units of flexural and dielectric strength.