1. CHEE 890J.S. Parent1 Static Testing of Polymers and Polymer Compounds Stress-strain analysis is the most widely used mechanical test. However, it is only a rough guide as to how a material will behave in a given application. Test specimens are prepared in the form of “dog bones” whose dimensions are known accurately: A static test involves deformation of the sample at a steady rate, usually with one end fixed and the other pulled at a constant rate of elongation (tensile testing). The retractive force of the material is recorded as a function of the elongation, and the engineering stress, , is calculated as a function of the engineering strain, .

2. CHEE 890J.S. Parent2 Static Testing of Polymers and Polymer Compounds We will soon see that observed polymer properties are strongly dependent on temperature and the applied rate of deformation. Under some conditions, an elastomer can behave like a brittle plastic, and vice-versa. Three typical behaviours are illustrated here. Often cited sample properties: A: Ultimate tensile stress (Pa) and elongation at break (%) B: Yield tensile stress, Pa Toughness: Area under  curve. A B A A

3. CHEE 890J.S. Parent3 Static Testing of Rubber Vulcanizates Static tensile tests measure retractive stress at a constant elongation (strain) rate.  Both strain rate and temperature influence the result Note that at common static test conditions, vulcanized elastomers store energy efficiently, with little loss of inputted energy.

4. CHEE 890J.S. Parent4 Fundamental Properties of Elastomers 1. The material must be macromolecular. 2. Must be amorphous (at least at low strains). 3. Tg must be below the operating temperature. 4. Must have low secondary forces between molecules so as to obtain the requisite flexibility. 5. A moderate degree of crosslinking must exist to establish anelastomeric network.

5. CHEE 890J.S. Parent5 Molecular Origin of Rubber Elasticity The conformation of elastomeric macromolecules is governed by: 1. Statistics of random processes (Brownian motion) 2. Preferences for sequences of bond arrangements due to steric and energetic associations. Vulcanized elastomers deform with virtually no change in volume, implying that mean interatomic distances do not change.  This is fundamentally different from the short-range elasticity of hard solids, where internal energy predominates

6. CHEE 890J.S. Parent6 Chain Conformation in the Unperturbed State A polymer chain can assume a large number of conformations. The end-to-end vector, r, therefore varies from 0 (touching) to a maximum that represents the fully extended (rod-like) form. It is often assumed that the distribution of r is well represented by the Gaussian function: where o is the mean square of the relaxed end-to-end distances. This function represents the probability that r exists between r and r+dr.

7. CHEE 890J.S. Parent7 Single Chain Elasticity If we restrict our system to a single polymer chain, we can use thermodynamic terms to derive its retractive force as a function of end-to-end distance, r.  Since we are interested in changes of thermodynamic properties with respect to temperature and dimension, the Helmholtz free energy (A) is the most convenient function. Application of the definition of the Helmholtz free energy (A) and the first law of thermodynamics yields: Therefore, the retractive force of an elastomer chain at a given temperature is the change in Helmholtz free energy with respect to dimension, r.

8. CHEE 890J.S. Parent8 Single Chain Elasticity To gain insight into how the Helmholtz energy of a chain varies with end-to-end distance, we differentiate the defining relationship at constant temperature to give: Ignoring the small contribution of internal energy, we can relate the restorative force to the entropy of the polymer chain. The strain in a stretched elastomer is caused by a reduction in conformational entropy of the chain under stress.  As we stretch the chain further and further, the chain becomes more ordered.  the rate of entropy loss increases, resulting in a steady rise of the restorative force.

9. CHEE 890J.S. Parent9 Crosslinking - Elastomeric Networks In its natural state, rubber is not a useful engineering material. Left unmodified, an elastomer will flow under an applied force with little “memory” of its original structure. Crosslinking of the elastomers generates a 3-dimensional network  excluding impurities, a rubber band can be considered one huge molecule. In general, vulcanizates are generated from elastomers of molecular weights in the range of 100,000 g/mole to produce 10-20 crosslinks per primary molecule  The average molecular weight between crosslinks is the relevant parameter in a vulcanizate.

10. CHEE 890J.S. Parent10 Crosslinked Polymer Networks Vulcanization, curing and crosslinking are equivalent terms referring to the process by which individual polymer chains are transformed into a network.  Most vulcanizates have an average molecular weight of about 4,000-10,000 in between crosslinks.

11. CHEE 890J.S. Parent11 Vulcanization - Sulfur and Peroxide Chemistry Curative formulations are developed by trial and error. Sulfur cures provide a wide range of properties at low cost. Peroxides provide high-temperature stability and function on saturated polymers. Sulfur Cures: applied only to unsaturated materials Peroxide Cures: can be used on most every polymer

12. CHEE 890J.S. Parent12 Accelerated Sulfur Cures

13. CHEE 890J.S. Parent13 Vulcanization: Crosslink Density Targets Crosslink density is determined by the curative recipe. Rheometry and/or tensile testing defines the rate and ultimate state of cure, but dynamic mechanical analysis, abrasion resistance and compression set tests are needed.  Curative formulations must be optimized using a complete knowledge of mechanical properties. Effect of state of cure on tensile properties of a butadiene/styrene compound tested at 77°F.

14. CHEE 890J.S. Parent14 Thermoplastic Elastomers Tri-block (or more) copolymers consisting of a ‘soft’ elastomeric segment and two ‘hard’ amorphous blocks.  Under processing conditions, both segments are above Tg, allowing the material to flow.  On cooling, separation of the phases into two domain types creates physical crosslinks between molecules. Examples include:  polystyrene-block-polybutadiene-block-polystyrene  segmented polyurethanes - Spandex, Lycra

15. CHEE 890J.S. Parent15 Tensile Properties of Vulcanized Elastomers Elasticity of a polymeric network is derived from flexibility of conformation for chain segments between crosslinks.  Descriptions of stress-strain profiles consider the concerted motion of chain segments in response to the deformation. The goal is to accurately model the extension or compression ratio as a function of the tensile or compressive force, f. The theoretical curve is generated by a statistical thermodynamic approach.

16. CHEE 890J.S. Parent16 Tensile Properties of Elastomeric Compounds 1. Statistical Thermodynamics  The probability (and hence, the entropy) of a single chain conformation is derived as a function of end-to-end distance and translated into a network distribution M c = M n between crosslinks  = density  = stretch ratio, L/L 0 2. Phenomenological Approach: Mooney (1940), Rivlin (1948)  Developed by considering the mathematical relations between stresses for an isotropic, incompressible material. C 1, C 2 = empirical constants The advantage of the former approach is an ease of interpreting calculated model parameters, while the latter approach fits experimental data more accurately.

17. CHEE 890J.S. Parent17 Tensile Properties of Elastomeric Compounds Plot of  /(  -1/  2 ) versus  -1 for a range of natural rubber vulcanizates. Sulfur content increases from 3% to 4%, with time of vulcanization and other quantities as variables.

18. CHEE 890J.S. Parent18 Viscoelasticity-Dynamic Properties (Chapter 5, Fried) When the load applied to a polymeric material is time dependant, we need to consider not only its strength, but the extent to which inputted energy is dissipated (viscous) and retrieved (elastic) Vibration Dampening / Isolation  Engine mounts: allow for engine movement, and dampen vibration  Protective sports equipment: require comfortable (soft) padding with exceptional impact dampening. High Elasticity Applications  Tire treads / sidewalls of low modulus and high extensiblity, as well as low rolling resistance Polymer Melt Processing  Swelling of extruded polymers upon release from the die changes the dimension and surface perfection of the product.

19. CHEE 890J.S. Parent19 Dynamic Testing of Rubber Vulcanizates: Resilience Resilience tests reflect the ability of an elastomeric compound to store and return energy at a given frequency and temperature. Change of rebound resilience (h/h o ) with temperature T for: 1. cis-poly(isoprene); 2. poly(isobutylene); 3. poly(chloroprene); 4. poly(methyl methacrylate).

20. CHEE 890J.S. Parent20 Dynamic Mechanical Analysis of Polymers Industrial engineers do not evaluate the dynamic properties of polymers by bouncing rubber balls.  Examine the dynamic elasticity as a function of temperature and/or frequency.  Impose a small, sinusoidal shear or tensile strain (linear  region) and measure the resulting stress (or vice versa) In this example, the stress is out of phase with the strain by 45° (  /4 radians) Stress Strain

21. CHEE 890J.S. Parent21 Dynamic Mechanical Analysis of Polymers A. The ideal elastic solid A rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (  =E . Therefore, the imposed strain function:   sin  t) generates the stress response   sin  t)   sin  t) and the phase angle, , equals zero. B. The ideal viscous liquid A viscous liquid is incapable of storing inputted energy, the result being that the stress is 90 degrees out of phase with the strain. An input of:   sin  t) generates the stress response   sin  t  and the phase angle, , .

22. CHEE 890J.S. Parent22 Dynamic Mechanical Analysis of Polymers Being viscoelastic materials, the dynamic behaviour of polymers is intermediate between purely elastic and viscous materials.  We can resolve the response of our material into a component that is in-phase with the applied strain, and a component which is 90° out-of-phase with the applied strain, as shown below:

23. CHEE 890J.S. Parent23 Dynamic Mechanical Analysis of Polymers The dynamic analysis of viscoelastic polymers the static Young’s modulus is replaced by the complex dynamic modulus: E* = E’ + i E”  The storage (in-phase) modulus, E’, reflects the elastic component of the polymer’s response to the applied strain.  The loss (out-of-phase) modulus, E”, reflects the viscous component of the response. The ratio of the two quantities is the loss tangent, tan  = E”/E’, which is function of temperature, frequency and polymer structure.

24. CHEE 890J.S. Parent24 Viscoelasticity in Crosslinked, Amorphous Polymers Plots of log G’, log G” and tan  against log angular frequency (in radians per second) for a typical elastomer above its Tg; Poly(styrene-co-butadiene) lightly vulcanized with a peroxide cure. Note that at low frequencies the material has a low modulus and behaves elastically. As frequency is increased, the material becomes stiffer, and less capable of storing inputted energy (generates heat upon deformation). Loss modulus Storage modulus tan  = G” / G’

25. CHEE 890J.S. Parent25 Dynamic Characteristics of Rubber Compounds Why do E’ and E” vary with frequency and temperature?  The extent to which a polymer chains can store/dissipate energy depends on the rate at which the chain can alter its conformation and its entanglements relative to the frequency of the load. Terminal Zone:  Period of oscillation is so long that chains can snake through their entanglement constraints and completely rearrange their conformations Plateau Zone:  Strain is accommodated by entropic changes to polymer segments between entanglements, providing good elastic response Transition Zone:  The period of oscillation is becoming too short to allow for complete rearrangement of chain conformation. Enough mobility is present for substantial friction between chain segments. Glassy Zone:  No configurational rearrangements occur within the period of oscillation. Stress response to a given strain is high (glass-like solid) and tan  is on the order of 0.1

26. CHEE 890J.S. Parent26 Logarithmic plots of G’ and G” against angular frequency for uncrosslinked poly(n-octyl methacrylate) at 100°C (above Tg), molecular weight 3.6x10 6. Viscoelasticity in Uncrosslinked, Amorphous Polymers