Polymer Testing and Properties

Polymer property units

Every property of a polymer is reported in a unit that follows from its defining formula, so the unit alone often identifies the property. If you know the definition, you can check a match without memorising a table.

Electrical properties. Surface resistivity is the resistance measured between electrodes placed on the surface of a specimen, so it is expressed in ohms (Ω), often written as ohms per square. Volume resistivity is the bulk specific resistance, \rho_v = RA/L, so its unit is ohm-centimetre (Ω·cm). Electrical conductivity is the reciprocal of resistivity, \sigma = 1/\rho, so its unit is siemens per centimetre (S cm^{-1}). A resistivity in Ω·cm becomes a conductivity in S cm^{-1} when inverted.

Thermal expansion. The coefficient of linear thermal expansion, \alpha = \frac{1}{L}\frac{dL}{dT}, is a fractional change per degree, so its unit is K^{-1} (or °C^{-1}). Do not assign a length or resistance unit to a ratio of this kind.

Mechanical and dielectric properties. Flexural strength is a stress and is reported in MPa. Notched Izod impact strength is the energy absorbed per unit notch width, so its unit is J m^{-1} and it cannot be a stress. Dielectric strength is the breakdown field, reported in kV cm^{-1} or MV m^{-1}. Complex viscosity is a dynamic viscosity and is measured in Pa·s.

Solubility, modulus and energy density. The Hildebrand solubility parameter is the square root of cohesive energy density, \delta = (\Delta E_{\text{vap}}/V)^{1/2}, so its unit is (MPa)^{1/2}. Loss modulus is a stress and is expressed in Pa. Toughness is energy per unit volume, so its unit is J m^{-3}. Because 1\ \text{Pa} = 1\ \text{N m}^{-2} = 1\ \text{J m}^{-3} = 1\ \text{kg m}^{-1}\text{ s}^{-2}, a stress and an energy density share SI units, and a unit written in a different SI form may still be correct.

• ohm per square — the unit used for surface resistivity, based on the resistance between surface electrodes.
• ohm-cm — the unit of volume resistivity, \rho = RA/L.
• K^{-1} — the unit of a thermal expansion coefficient, a fractional change per degree.
• J m^{-1} — energy per unit length, as in notched impact strength.

Stress-strain behavior of polymers

The engineering stress-strain curve of a polymer is read in stages. It begins with a linear elastic region whose slope is Young's modulus E. Depending on the polymer, it then shows a yield point, necking or cold drawing, strain hardening, and finally fracture. In the elastic region Hooke's law gives \sigma = E\varepsilon, so the strain is \varepsilon = \sigma/E. Strain is dimensionless, so stress and modulus must be in the same unit before dividing.

Three groups of polymers are easy to recognise from their curves.

• Brittle glassy polymers such as polystyrene have high modulus, little or no yield, and fracture at small strain.
• Semicrystalline thermoplastics such as polyethylene show a yield point followed by necking. Oriented nylon fibres have high yield strength and undergo cold drawing.
• Vulcanized rubber is an elastomer. It has a low modulus, very large recoverable elongation, and a rise in stress at high strain as the network stretches.

Fibre-reinforced composites follow the same logic. Glass fibre is stiff and brittle, so its curve is the steepest and ends at a small strain. The polymer matrix has the lowest modulus. A unidirectional lamina loaded along the fibres forces fibre and matrix to share the same strain, so its longitudinal modulus follows the rule of mixtures, E_c = V_f E_f + V_m E_m. The composite curve therefore lies between the fibre and matrix curves.

• Young's modulus — the slope of the linear elastic region; a steeper slope means a stiffer material.
• yield point — the stress at which permanent plastic deformation begins.
• necking — a local reduction of cross-section in a ductile polymer under tension.
• cold drawing — stable plastic extension at a nearly constant stress, typical of oriented fibres.
• rule of mixtures — a linear weighting of fibre and matrix properties by volume fraction, used for the longitudinal modulus.

Mooney viscosity measurement

Mooney viscosity is an empirical measure of the processability of unvulcanized rubber, obtained with a Mooney viscometer. A metal rotor is enclosed in a heated die cavity filled with the rubber sample. The torque required to turn the rotor at a fixed speed is recorded in Mooney units (MU). Because it is a torque reading for one specific geometry, Mooney viscosity is not a true viscosity and has no SI unit.

The standard notation is written like ML(1+4) 100 °C, and each part has a fixed meaning.

• M — Mooney viscosity.
• L — the large rotor; the small rotor is denoted S.
• 1 — the preheat time in minutes at the test temperature, before the motor starts.
• 4 — the running time in minutes after the motor is started. The torque is read at the end of this period.
• 100 °C — the test temperature.

For example, ML(1+8) 125 °C describes a sample preheated for one minute, run for eight minutes, and tested at 125 °C. The running time must be read from the notation, not the preheat time, when the question asks what a number signifies.

Stress-strain toughness

Toughness is the energy a material absorbs per unit volume before it fractures. Under a tensile test it equals the area under the engineering stress-strain curve, U_T = \int_0^{\varepsilon_f}\sigma\,d\varepsilon, whose unit is J m^{-3}. A material that is strong but breaks at a small strain can have a smaller area than a less strong but more extensible polymer, so strength alone does not indicate toughness.

Impact tests give a related measure. The Izod and Charpy tests record the energy absorbed in breaking a notched specimen under a sudden blow, so they are standard indicators of toughness. Depth of indentation is different: it measures resistance to local penetration, which is hardness. A hard polymer is not necessarily tough, and a tough polymer is not necessarily hard.