On the basis of the curves in Figure \(15.5\), sketch schematic strain-time plots for the following polystyrene materials at the specified temperatures: (a) Crystalline at \(70^{\circ} \mathrm{C}\) (b) Amorphous at \(180^{\circ} \mathrm{C}\) (c) Crosslinked at \(180^{\circ} \mathrm{C}\) (d) Amorphous at \(100^{\circ} \mathrm{C}\).

In order to sketch schematic strain-time plots, we first need to understand the behaviors of different types of polystyrene materials at different temperatures: 1. Crystalline: This type of material has a well-ordered structure and undergoes a phase transition (melting or crystallization) at a specific temperature. It shows elastic behavior at low temperatures and viscous flow (liquid-like) behavior at high temperatures. 2. Amorphous: This material lacks an ordered structure and undergoes a glass transition at a specific temperature. It shows glassy, brittle behavior at low temperatures and rubbery, elastic behavior at high temperatures. 3. Crosslinked: This type of material has covalent bonds (crosslinks) between polymer chains, which restrict the chains' motion. It shows elastic behavior with temperature-independent rubbery characteristics.

(a) Crystalline at \(70^{\circ}\mathrm{C}\) At this temperature, the crystalline polystyrene is expected to show elastic behavior as it should be below the phase transition temperature. The strain-time plot should resemble a straight line with a slope, demonstrating a linear relationship between strain and time. (b) Amorphous at \(180^{\circ}\mathrm{C}\) At this temperature, the amorphous polystyrene is expected to be in the rubbery state since it should be above the glass transition temperature. The strain-time plot should resemble a sigmoid curve. It begins with a steep slope indicating the elasticity and becomes less steep as the sample goes through a rubbery plateau region before steeply increasing again due to the viscous flow. (c) Crosslinked at \(180^{\circ}\mathrm{C}\) With crosslinked polystyrene, temperature has a minimal effect on its behavior. So even at \(180^{\circ}\mathrm{C}\), it should exhibit elastic behavior. The strain-time plot should resemble a straight line with a slope similar to the crystalline polystyrene, representing a linear relationship between strain and time. (d) Amorphous at \(100^{\circ}\mathrm{C}\) At this temperature, the amorphous polystyrene should be in a glassy, brittle state since it is below the glass transition temperature. The strain-time plot should show a sharp increase in strain until reaching a critical point at which the material would fracture. The plot may approximately resemble a steep linear line in the beginning which will have a sudden increase in slope due to the brittle nature of the material.