Some polymers are tough, while others are strong. When designing new materials, one often has to make trade-offs between strength and toughness. One may have to sacrifice a little strength so a product will be tougher, for example.
But sometimes we can combine two polymers with different properties to get a new material with some of the properties of both. There are three main ways of doing this, and they are making copolymers, blending, and making composite materials.
An example of a copolymer that combines the properties of two materials is spandex. It's a copolymer containing blocks of elastomeric polyoxyethylene and blocks of a rigid fiber-forming polyurethane. The result is a fiber that stretches. Spandex is used to make stretchy clothing like bicycle pants.
High-impact polystyrene, or HIPS for short, is an immiscible blend that combines the properties of two polymers, styrene and polybutadiene. Polystyrene is a rigid plastic. When mixed with polybutadiene, an elastomer, it forms a phase-separated mixture that has the strength of polystyrene and the toughness of polybutadiene. For this reason, HIPS is far less brittle than regular polystyrene.
In the case of a composite material, we're usually using a fiber to reinforce a thermoset. Thermosets are crosslinked materials whose stress-strain behavior is often similar to plastics. The fiber increases the tensile strength of the composite, while the thermoset gives it compressional strength and toughness.
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