Overview

Our last lesson of this course is focused on the mechanical properties of polymers. While we will be largely discussing the macroscale properties of polymers, always be mindful of how those bulk properties are actually derived from the molecular scale structure and chemistry of the polymer. In order to motivate how important it is to understand the mechanical properties of polymers and how that relates to molecular scale polymer structure and dynamics, consider the tragic accident of the Challenger explosion. Polymeric O-ring seals, which are flexible and elastic, were used in the space shuttle at joints where it was necessary to contain and compartmentalize explosive propellant. The day of the shuttle launch, it was quite cold, with temperatures dropping below the glass transition temperature of the polymer O-rings. The low temperatures caused the O-rings to become brittle, non-elastic, and glassy, as we well know should happen when a polymer is below $T_g$. Thus, the O-rings could not form a tight seal, and upon launch, the joints failed and the Challenger exploded. This accident highlights how critical it is for you – the future scientists and engineers – to learn the fundamental chemistry and mechanics of the materials you work with. For more information, read the O-ring Concerns section of the Wikipedia Space Shuttle Challenger Disaster page

Polymers are a unique class of materials in terms of their mechanical properties because they may possess some characteristics of a fluid and some characteristics of a solid. While ideal elastic solid materials store all the energy from stress in the bonds, so that the material will restore itself upon release of stress, ideal viscous fluids dissipate all the stress in flow. Polymers, as we will see, tend to be somewhere in the middle. We have a special term to describe this combination of fluid and solid properties: viscoelasticity.

Figure 12.1: Viscoelastic properties

Source: Lauren Zarzar

Learning Outcomes

By the end of this lesson, you should be able to:

• Describe the stress-strain characteristics of elastomers, glassy polymers, semi-crystalline polymers.
• Correlate chemical structure with mechanical properties.
• Explain the changes in entropy and enthalpy that occur during elastomer deformation.
• describe strain induced crystallization and hysteresis.
• Draw time dependent strain plots for viscoelastic material.
• Analyze modulus vs time plots and identify glass region, glass transition, rubbery plateau.
• Compare mechanical properties for low and high molecular weight polymers; crosslinked and non-crosslinked polymers.
• Describe how mechanical properties of polymers depend on temperature.
• Define shear thinning and shear thickening polymers.
• Describe how molecular weight affects viscosity.

Lesson Checklist

Please refer to the Canvas Calendar for specific timeframes.

Questions?

If you have questions, please feel free to post them to the General Questions and Discussion forum. While you are there, feel free to post your own responses if you, too, are able to help a classmate.

First, let’s consider polymers as solids. When we treat a polymer like a solid, we consider things like the strength, stiffness, and toughness of a material. Hooke’s law is relevant here (stress = Young’s modulus x strain):

$$\sigma =E\epsilon$$

Stress, $\sigma$, the load on an object divided by its cross-sectional area, is a measure of the force at any point inside a material (much like how we describe the pressure exerted by a gas on the walls of its container). Stress therefore equals force divided by area:

$$stress=\sigma =\frac{force}{area}$$

Strain is defined as the normalized extension, the change in length ($\Delta l$) divided by the original length of the object ($l_0$).

$$strain=\epsilon =\frac{\Delta l}{l_0}$$

Stress is proportional to the stain and independent of loading rate. If we plot stress versus strain, then the modulus of the material is the slope of the curve, toughness is the area under the curve, and strength is the stress at breaking. This relationship for an ideal elastic solid is shown below.

Figure 12.2: Modulus of an ideal elastic solid

Source: Lauren Zarzar

Think about how these properties could tie back to the molecular scale. We basically have a series of atoms linked up together by a network of bonds, which are a little like tiny springs (and thus we can more easily visualize how Hooke’s law is relevant here). Stiffness or modulus of a solid material is related to the stiffness of the chemical bonds within the system (how much does the spring stretch?). Strength of an ideal solid material is related to the cohesive strength of the bonds, which is proportional to the depth of the potential energy well of the bonds.

For an ideal elastic solid, if we apply and subsequently remove a force on the material, it should go back to its original shape without any permanent deformation. There is no perfectly elastic material. When it comes to polymers, probably the closest we can come are single crystals of polymers, which are rare.  “Real” solid materials deviate from such ideal behavior.

Figure 12.3: Mechanical propertiesof polymers

Source: Figure 19.4 and Table 19.1 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Above are some examples of how varied the mechanical properties of polymers can be. The breaking points for materials on this plot is shown with the “x”. Polymer fibers which are crystalline can be high modulus, and so can glassy polymers below $T_g$. But semi-crystalline polymers and elastomers (above $T_g$) are “softer” and certainly have lower modulus. Thus, the mechanical properties are highly tunable and span orders of magnitude in scale. Comparing the modulus of some common polymers to other materials (Table 12.1 below) we see that polymers, in comparison, are not very stiff! Even a glassy polymer like atactic polystyrene has a modulus of only about 3,000 MPa  (about 1/20^th that of window glass).

Why are the mechanical properties of polymers so variable, and why so different than other solid materials? Polymers are unique in that they are made of giant molecules – these molecules interact very differently than small molecules. Many factors affect polymer mechanical properties. Some of these we already discussed in detail. $T_g$ for example, by definition, is a change in the mechanical properties. Above the glass transition, polymers can flow and deform with lower modulus, but below the glass transition, polymers are glassy solids and are more brittle. Cross-linking most definitely affects mechanical properties; thermosets are characterized by very high levels of crosslinking, and they tend to be more rigid and higher modulus than a low-crosslinking elastomer. Crystallinity is a big factor as well. Consider the difference in modulus between and high and low density PE in the table above. Recall that HDPE is linear, and the chains pack together much more easily. Whereas for LDPE, there is branching which prevents close packing, and prevents crystallization, of the PE. Because HDPE has more crystallinity, we find that its modulus is much higher.  

We have already stated that single-crystal polymers are very rare; semi-crystalline polymers, which have some amorphous and some crystalline regions, are much more common. If the polymer is semi-crystalline, then it has some regions that are crystalline and some that are amorphous and the mechanical properties of the bulk tend to be a combination or “average” of the properties associated with each. So for example, we expect crystalline polymers to have higher modulus and amorphous polymers to have lower modulus, thus as we increase the degree of crystallinity, we find that the modulus also increases:

Figure 12.4: Variations of Young's modulus (E) with the degree of crystallinity for different polymers

Source: Figure 19.9 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.

Even within polymers that are the same “chemically”, i.e., polyisoprene, we can still have geometric isomers and/or different skeletal structure that influence the mechanical properties. For example, “cis” isomers tend to not pack together well, and therefore do not crystallize to a significant degree. Thus, polyisoprene that is predominantly in the “cis” conformation is an elastomeric material. But the “trans” form does pack better, induces more crystallization, and causes the material to be more rigid. You could thus imagine tuning the overall mechanical properties of this polymer by just varying the ratio of cis and trans bonds in the polymer.  

Figure 12.5: cis and trans bonds of 1,4-polyisoprene

Source: Lauren Zarzar

Given the unique mechanical properties of elastomers, it’s worth considering the thermodynamics associated with mechanical deformation. Try this at home! Hold a rubber band to your lips and stretch it, then release it. Do you feel a change in temperature? When you stretch the rubber band, you should feel heat (exothermic, $\Delta H$ is negative). When you release the rubber band, you feel cool (endothermic, $\Delta H$ positive). What’s going on, and can we explain it in terms of entropy and enthalpy?

Strain induced crystallization means that polymer chains become more aligned when stretched, facilitating crystallization (which contributes to the exothermic nature of the rubber band stretching!) This isn’t necessarily a good property….. We know that the degree of crystallinity of a polymer can have dramatic impact on its mechanical properties. So if the degree of crystallinity changes, then the properties, change, perhaps in undesirable ways. It also means the polymers behave differently upon application and release of stress (hysteresis) (see Figure 12.6 below).

Figure 12.6: Illustration of mechanical hysteresis for a strain-crystallizing elastomer

Source: Figure 21.9 from Young, Robert J., and Peter A. Lovell.
Introduction to Polymers, Third Edition, CRC Press, 2011.
(Data taken from Andrews, E.H., Fracture in Polymers, Oliver and Boyd Ltd. London, 1968)

Previously, we treated polymers as solid. Now, we are focusing on polymers as liquids. Viscosity is a characteristic property of fluids; a less viscous fluid has low resistance to shear stress, while a highly viscous fluid has higher resistance to shear stress. We have intuition about this – water we would consider to have low viscosity, while something like toothpaste would be highly viscous. The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress. Imagine a sandwich with two plates on either side and a fluid in between. If you push one plate and keep the other static, what happens to the liquid? The plates do not simply slide past the fluid – but rather the liquid is “stuck” at the walls, and is “sheared” when you slide the plates past each other. There is some frictional force in the fluid. This is viscosity.

Figure12.7: laminar shearing of fluid

Source: Wikipedia: Viscocity

Ideal viscous fluids, i.e. Newtonian fluids, have a viscosity ($\eta$) that is independent of shear rate ($\dot{\gamma }$) such that this relationship between shear stress ($\tau$), viscosity, and shear rate would yield a constant value of viscosity no matter what shear is applied:

$$\tau =\eta \dot{\gamma }$$

Figure12.8: Plot of a Newtonian fluid

Source: Lauren Zarzar

Many liquids that consist of small molecules, like water for example, may not be “perfect” Newtonian fluids, but they come pretty close. When we consider polymeric fluids, which could be a polymer melt or a polymer solution, the fact that there are very large polymer molecules now impart significantly different properties to the fluid; most polymer melts are therefore non-Newtonian fluids.

If a fluid is non-Newtonian, then there clearly must be some dependence of the viscosity on the shear rate. There are two general possibilities for how the fluid might behave: either the material increases in viscosity with increasing shear rate, or the viscosity decreases with an increasing shear rate. These are called shear thickening or shear thinning fluids, respectively. A diagram that considers how the shear stress - shear rate curves for shear thinning and shear thickening polymers might look is shown in Figure 12.9. The slope of these shear stress – shear rate curves is called the apparent viscosity, ${\eta }_a$.

Figure12.9: Shear stress - shear rate curves for shear thinning, shear thickening and Newtonian fluids

Source: Lauren Zarzar

An example of a shear thickening material is Ooobleck (which is cornstarch in water) or wet sand. But actually most polymer melts and solutions are shear thinning. Ketchup is a great example of a shear thinning fluid; it will almost certainly never come out of the bottle in any reasonable time if you just turn it upside down, but if you give the bottle a good shake (=shear) suddenly it starts to flow!

PROBLEM

Which plot below shows a shear thinning fluid?

Click here for the answer.

ANSWER

Plot C.

The viscosity is just the slope of the shear stress – shear rate plot. A fluid that increases viscosity with increasing shear rate is shear thickening, while a fluid that decreases viscosity with increasing shear rate is shear thinning. Shear thinning is common in polymers.

Looking back at the plots of shear stress vs shear rate in Figure 12.9, we notice that while at higher shear rates, the apparent viscosity changes rapidly, at low shear rates, the viscosity can actually be relatively constant.  The constant apparent viscosity in the low-shear region is known as the zero shear viscosity, ${\eta }_0$.

The viscosity of polymer melts depends on a number of factors. An important factor is the molar mass. The plot below shows the $Log\left( {\eta }_0\right)$ vs $Log(degreeofpolymerization)$ for a range of different polymers.

Figure12.10: $\mathrm{Log}{\eta }_0$ vs $Log(degreeofpolymerization)$ for a range of different polymers.

Source: Lauren Zarzar (Redrawn from the data of G. C. Berry and T. G. Fox, Adv. Polym. Sci., 5, 261 (1968))

You’ll notice that viscosity increases with molecular weight (which is directly related to degree of polymerization) – by orders of magnitude. Now at first glance, given that the viscosity of the polymers increases so dramatically with molecular weight, we might think that high molecular weight polymers are orders of magnitude harder to process. Actually, because of shear thinning, it’s not as difficult as you might think. Which brings us to the question of why is a polymer shear thinning in the first place? Again, we come back to entanglements!  As you shear a polymer along a specific direction, the polymers slip past each other and there is some disentanglement and actually the polymer chains align in the direction of shear. This polymer alignment during shear actually is very important to the mechanical properties of the polymer products being manufactured because it can impart different mechanical properties along different axes of a material. For example, if you have ever tried ripping a plastic grocery bag along different directions, you’ll notice that in one direction it tears easily, while along the perpendicular direction it is much more difficult – and it is because of polymer alignment during shear imposed during the manufacturing of the bag itself.

Figure12.11: Ploymer alignment with no shear and under shear

Source: Lauren Zarzar

PROBLEM 2

Sample A and Sample B are the same type of linear polymer but different molar weight. You analyze the samples with SEC and obtained the chromatogram below. Which sample has higher viscosity?

Click here for the answer.

ANSWER 2

Sample A

Recall learning about SEC and how higher molecular weight polymers will elute faster than lower molecular weight polymers (all else equal). Thus, Sample A is the higher MW polymer and we would expect it to have the higher viscosity.

Viscoelasticity combines a little bit of both solid behavior and fluid behavior. While ideal elastic materials store all the energy from stress in the bonds, so that the material will immediately restore itself upon release of stress, ideal viscous fluids dissipate all the stress in flow. Viscoelastic materials are somewhere in the middle, and many polymers are viscoelastic. An important characteristic of viscoelastic materials is that timescale matters. For ideal elastic solids and ideal viscous liquids, time doesn’t matter – whether you apply a stress fast or slow, the response of the material should be identical. But this isn’t so for most polymers, which show time-dependent behavior. Two important time-dependent properties of polymers are creep and stress relaxation.

Creep is a property of viscoelastic materials in which the strain of the material changes over time while under a constant load (stress) (Figure 12.12). Creep is not something that happens in a perfectly elastic solid. For an ideal elastic material, under constant stress, it would instantaneously deform and would also instantaneously go back to original shape after removal of stress.

Figure 12.12: Creep of a viscoelastic material while under a constant stress

Source: Lauren Zarzar

A strain vs. time plot for a viscoelastic material with creep would likely look something like this:

Figure 12.13: creep and recovery in a viscoelastic material

Source: Lauren Zarzar

The creep can be non-linear, as shown, where the strain changes in a non-linear fashion with time. Upon release of the stress, the polymer can recover some, but usually undergoes some amount of permanent deformation.

In comparison to creep, which is a constant stress experiment, stress relaxation is a constant strain experiment. You deform the material to a given strain, and measure the stress required to maintain that deformation over time (Figure 12.14).

Figure 12.14: Stress relaxation under constant strain

Source: Lauren Zarzar

The data for stress relaxation experiments are usually reported as a modulus vs time plot. This time dependent modulus, called the relaxation modulus, $E\left( t \right)$, is simply the time dependent stress $\sigma \left( t \right)$, divided by the (constant) strain, ${\epsilon }_0$:

$$E\left( t \right)=\frac{\sigma \left( t \right)}{{\epsilon }_0}$$

Importantly, stress relaxation is also temperature dependent. The graph shows how PMMA relaxation modulus varies as function of both time and temperature. As expected, the relaxation modulus goes down with time – after all, if at constant strain the stress is decreasing, then the modulus must be decreasing too. We also see that at higher temperatures, the modulus is also lower. This makes sense, as we are heating the polymer, we supply more energy for those bonds to rotate, for the polymers to move past each other, to overcome intermolecular interactions – thus, the modulus will decrease.

Figure 12.15: PMMA relaxation modulus

Source: Lauren Zarzar (Redrawn from the data of J.R. McLoughlin and A.V. Tobolsky. J. Colloid Sci., 7, 555 (1952))

An important characteristic of viscoelastic materials is the time-dependent mechanical properties. At short time scales, a polymer may behave as a glassy solid, but at longer time scales, it could flow more like a liquid. This time dependence is influenced by things like molecular weight which affects entanglements, as we touched on in the “polymers as liquids” section (Figure 12.16 below). If you have a low molecular weight polymer it will form less entanglements and so “untangles” more quickly. Larger polymers take longer to relax and untangle, and we see this in the “rubbery plateau” region of the plot below. A nice example of the impact of these time-dependent properties is silly putty. Silly putty behaves like an elastic solid on short time scales – you can bounce it like a rubber ball. But at long time scales, for instance if you just leave it out on the table, it flows like a liquid and will spread.

Figure 12.16: impact of polymer molecular weight on the relaxation modulus

Source: Lauren Zarzar

The plots above are a function of time, but we also know that stress relaxation should also be affected by temperature.

PROBLEM

In the figure below, we consider the effect of temperature on the modulus for polymers at a given time and strain. We already know that going from below to above the glass transition temp will have a dramatic effect on the modulus – below $T_g$ the polymer is rigid glassy solid, but above $T_g$ it begins to flow and the modulus decreases significantly. Both plots shown are for high molar mass polymer, and hence both have a rubbery plateau, but one sample is crosslinked and one is linear. Which one is which?

Click here for the answer.

ANSWER

Plot (a) is linear and plot (b) is crosslinked. The crosslinked polymer reaches a limit of lower modulus because it is being held together by crosslinks that prevent the network from deforming indefinitely.

So how do we turn polymers into the products that we use in our daily lives, and how do these mechanical properties influence the processability of polymers? Definitely, we need to keep in mind how the skeletal structure of the polymer will affect the general mechanical properties (i.e., a highly crosslinked thermoset is going to be processed somewhat differently than a linear thermoplastic). But, in general, processing methods have three phases:

1. heating to soften or melt
2. shaping/forming under constraint
3. cooling to retain shape

The most common processing approaches are injection molding, extrusion, blow molding (these three are mostly useful for thermoplastics) and compression molding (more useful for thermosets). Because it is so much easier to see how processing is done through video, please watch this video (6:08) which summarizes the most common approaches to polymer processing:

Most polymer products you use on a day to day basis are made by injection molding. If you are interested, I highly suggest watching this interesting video (9:36):

Summary

In this lesson, we have covered many of the common characterization techniques (DSC, SEC, end group analysis, etc.) that are used to analyze various properties of polymers (thermal transitions, molar mass distributions, number average molar mass, etc.). These techniques are by no means the only ones and in particular, we did not discuss spectroscopy, which encompasses so many important characterization techniques.

In the next lesson, we will be learning about mechanical properties of polymers. Polymers have some very unique mechanical properties and can differ significantly from materials you likely learned about in MatSE 201. Even though we will be talking mostly about properties of “bulk” polymers, don’t forget that the molecular scale chemistry, bonding, and intermolecular interactions, and chain conformations that we spent so much time learning about – these things are all at the core of WHY polymers have certain bulk properties.

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