CHEE 890 J.S. Parent 1

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, .

Pa:AF

o

oLL

CHEE 890 J.S. Parent 2

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 areillustrated 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

CHEE 890 J.S. Parent 3

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.

CHEE 890 J.S. Parent 4

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 asto obtain the requisite flexibility.

5. A moderate degree of crosslinking must exist to establishan elastomeric network.

CHEE 890 J.S. Parent 5

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

CHEE 890 J.S. Parent 6

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 <r2>o is the mean square ofthe relaxed end-to-end distances.

This function represents the probability that r exists between r and r+dr.

2

o

2

22/3

o

2r4

r2

r3exp

r2

3)r(W

CHEE 890 J.S. Parent 7

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.

TrA

f

CHEE 890 J.S. Parent 8

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.

T T T

A U ST

r r r

T

Sf T

r

CHEE 890 J.S. Parent 9

Crosslinking - Elastomeric Networks

In its natural state, rubber is not a useful engineering material. Leftunmodified, an elastomer will flowunder an applied force with little“memory” of its original structure.

Crosslinking of the elastomers generatesa 3-dimensional network

excluding impurities, a rubberband can be considered onehuge molecule.

In general, vulcanizates are generatedfrom elastomers of molecular weightsin 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.

CHEE 890 J.S. Parent 10

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.

CHEE 890 J.S. Parent 11

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

Sx S8 ZnOaccelerators 145C

ROOR 145C

CHEE 890 J.S. Parent 12

Accelerated Sulfur Cures

CHEE 890 J.S. Parent 13

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.

CHEE 890 J.S. Parent 14

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

CHEE 890 J.S. Parent 15

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 accuratelymodel the extension orcompression ratio as a function of the tensile orcompressive force, f.

The theoretical curve isgenerated by astatistical thermodynamicapproach.

CHEE 890 J.S. Parent 16

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

Mc = Mn between crosslinks = density = stretch ratio, L/L0

2. Phenomenological Approach: Mooney (1940), Rivlin (1948) Developed by considering the mathematical relations between

stresses for an isotropic, incompressible material.

C1, C2 = 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.

2

cstress

1

M

RT

2

21stress

1CC2

CHEE 890 J.S. Parent 17

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.

CHEE 890 J.S. Parent 18

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.

CHEE 890 J.S. Parent 19

Dynamic Testing of Rubber Vulcanizates: Resilience

Resilience tests reflect the ability of anelastomeric compound to store andreturn energy at a given frequency and temperature.

Change of rebound resilience (h/ho) with temperature T for:

1. cis-poly(isoprene);

2. poly(isobutylene);

3. poly(chloroprene);

4. poly(methyl methacrylate).

CHEE 890 J.S. Parent 20

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

CHEE 890 J.S. Parent 21

Dynamic Mechanical Analysis of Polymers

A. The ideal elastic solidA rigid solid incapable of viscous dissipation of energy follows Hooke’s Law, wherein stress and strain are proportional (=E. Therefore, the imposed strain function:

sint)generates the stress response

sint)sint)and the phase angle, , equals zero.

B. The ideal viscous liquidA 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:

sint)generates the stress response

sintand the phase angle, , .

CHEE 890 J.S. Parent 22

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:

CHEE 890 J.S. Parent 23

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.

CHEE 890 J.S. Parent 24

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’

CHEE 890 J.S. Parent 25

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 tanis on the order of 0.1

CHEE 890 J.S. Parent 26

Logarithmic plots of G’ and G” against angular frequency for uncrosslinked poly(n-octyl methacrylate) at 100°C (above Tg), molecular weight 3.6x106.

Viscoelasticity in Uncrosslinked, Amorphous Polymers