Viscoelasticity is a phenomenon of fundamental importance in the understanding of the behavior of polymeric materials. Mechanical properties of polymers are of course temperature-dependent, but are also time-dependent. It is useful to visualize this aspect as a prelude to a more sophisticated understanding of viscoelasticity. We present a simple system, namely rubbery bilayers with one layer exhibiting time-dependent behavior, as an exemplary illustration of viscoelasticity using commercially-available materials. Various bilayer configurations can exhibit interesting and reversible shape changes upon application and release of tension, and readers are encouraged to expand upon the behaviors of a few examples presented.
Figure 1. Comparison of stress-strain behavior for elastic and hyper-elastic materials
Elastomers, such as a common rubber band, are characterized by rapid retraction after stretching and subsequent release of strain. Key characteristics to achieve the familiar properties of elastomers include a high molecular weight, a use temperature which is above the polymer’s glass transition temperature or Tg, little to no crystallinity, and light crosslinking [1, 2]. The latter can be covalent (e.g., sulfur crosslinks in a typical ‘vulcanized’ rubber, such as a rubber band) or physical, such as glassy polystyrene domains in thermoplastic elastomers or TPEs (e.g., poly(styrene-b-isoprene-b-styrene)), or hydrogen-bonded hard segments in thermoplastic polyurethanes (TPUs) such as Lycra fiber. The crosslinks act to inhibit permanent sliding of chains past each other during stretching. The retraction of a stretched rubber band is driven largely by entropy, where oriented chains can quickly revert to Gaussian random coils in the unstretched condition. It is tempting to suggest that a simple mechanical model for an elastomer would be a spring with a rather low modulus or spring constant. However, an elastomer stress-strain curve has a characteristic S-like shape (Figure 1), and represents what is termed neo-Hookean or hyperelastic behavior. To simplify our discussion, we can consider an elastomer to be elastic. Consistent with experience, retraction of a stretched elastomer to its initial dimensions upon release of stress will be rapid.
In the absence of crosslinking, the behavior under a tensile stress is quite different. It is in fact time-dependent, exhibiting key characteristics of viscoelasticity such as creep and stress relaxation [3, 4]. For example, unvulcanized cis-1,4-polyisoprene, which is natural rubber, will appear to snap back if a sample is stretched followed quickly by release of strain, but will creep (permanent strain with constant applied stress) if stretched for longer periods of time. The quick retraction is due to the presence of physical chain entanglements which, like crosslinks, serve to restrict permanent reorganization and flow of chains. However, entanglements can serve in this capacity only on relatively short time scales. Longer application of stress will indeed lead to permanent viscous flow of chains relative to one another, and a permanent strain after the stress is removed. This is an example of creep. A related phenomenon is stress relaxation, which is the measured decrease of applied stress at a constant strain. Once again, permanent disentangling and subsequent relief of stress at constant strain can occur in the absence of crosslinks. An example of a particularly fast stress-relaxing material is Silly PuttyTM, where it is easy to ‘feel’ stress relaxation in a few seconds.
Figure 2. Simple viscoelastic models. a) Maxwell model and b) Kelvin-Voigt model
The simplest mechanical model for stress relaxation is the Maxwell model, with a spring (and an attendant spring constant) and a dashpot in series (Figure 2a).
A dashpot is a viscous element, a fluid-filled piston characterized by a viscosity, η, whereas the elastic spring is associated with a spring constant or stiffness, frequently labeled E. Imagine instantaneous stretching of a Maxwell element to a fixed strain. The spring will stretch instantly, but the dashpot will extend more slowly, the time scale being determined by the viscosity of the dashpot fluid. The result is an exponential decay of stress as the dashpot extends and the spring retracts. While the Maxwell model is able to describe stress relaxation, it is unable to describe creep. When the Maxwell element is subjected to a fixed stress the dashpot will keep elongating. Upon removal of the stress the elastic spring will recover but the dashpot will remain excessively deformed, causing an overestimation of any permanent strain caused by creep. By rearranging the elastic spring and dashpot into a parallel configuration, the Kelvin-Voigt model is formed (Figure 2b). The Kelvin-Voigt model is able to describe creep because the spring that is in parallel with the dashpot prevents the dashpot from deforming excessively. As the dashpot elongates the spring counteracts the elongation with a greater retracting force until an equilibrium strain is reached. Conversely, the Kelvin-Voigt model is unable to describe stress relaxation, as its dashpot prevents the Kelvin-Voight element from being instantaneously stretched to a fixed strain.
It would be surprising that a single Maxwell or Kelvin-Voigt element could appropriately model the behavior of a real polymeric material, and thus a generalized Maxwell model (Figure 3), with different values of spring constants and viscosities, is more realistic. Interestingly, the stress relaxation of Silly PuttyTM has been modeled using three Maxwell elements in parallel, a combination that captures well the experimental data [5]. The behavior of viscoelastic materials such as Silly PuttyTM or unvulcanized butyl rubber (essentially poly(isobutylene), PIB) can be appreciated by considering the dimensionless Deborah Number, De, [6] defined as the ratio of a characteristic relaxation time, τ, of say unvulcanized butyl (roughly the time required to relieve an imposed stress via a combination of chain segment movement, thermal vibrations and bond rotations) to the observation time, t:
Figure 3. Generalized Maxwell Model
De = τ/t
We recently reported on a detailed study of mechanical responses of bilayers of vulcanized vs. an unvulcanized rubber [7], and it occurred to us that simple, qualitative experiments using such bilayers could be useful in facilitating an appreciation of basic viscoelastic principles. A polymer pair that we especially like is unvulcanized butyl, which will normally stress-relax, adhered to poly(styrene-b-isobutylene-b-styrene), SIBS, a TPE that will quickly retract.
Butyl [8] | SIBS |
It is important to have good adhesion between the two materials to prevent delamination and enable the bilayer to respond as a cohesive unit, which is expected given that the center block of the TPE is butyl. The presence of similar repeat units will promote adhesion through the formation of intermolecular entanglements.
The experiment involves manual stretching of a bilayer strip to a nominal strain of about 300%, holding for say 10 seconds, and then releasing the strain. Before discussing the steps to fabricate bilayers and to qualitatively observe their interesting mechanical behavior, let us attempt to rationalize what might happen in advance with the aid of illustrative graphics. Stretching of the TPE and holding for several seconds, followed by release of strain, is expected to show immediate retraction as expected from an elastomer as shown below, approximated by springs (Figure 4a).
Figure 4a. Graphic of reversible stretching and retraction of an elastomer such as SIBS using a spring analogy
An attached layer of butyl is modeled as a spring and dashpot in series (Maxwell model) adhered to a spring to represent the elasticity of the SIBS layer (Figure 4b). Upon stretching, holding at constant strain for a few seconds, and finally release of strain, competition ensues between the TPE’s desire to retract and the butyl’s desire to slowly flow and its chains to reorganize. What actually does happen? Upon release of a tensile strain, the strip will bend and also curl given the sluggish response of the butyl layer. However, the butyl, bonded well to the TPE, has little choice but to eventually return to original dimensions, but on its own slower terms.
Figure 4b. Graphic of stretching, bending and eventual retraction of a bilayer (SIBS as a spring, and butyl as a spring and dashpot in series)
Figure 5. A Zener viscoelastic model
Figure 4b is an example of what is termed a Zener model, with a spring in parallel with a Maxwell element (Figure 5). Note that Maxwell elements can be added in parallel to construct a variant that is a generailzed Maxwell model (Figure 3) with a parallel spring.
Let’s attempt to understand these concepts through observations with easy-to-fabricate bilayers.
SIBS (SIBSTARTM 073T, 102T or 103T from Kaneka Co.) [9] and butyl (Butyl 268 from ExxonMobil Co.) are recommended, but other thermoplastic elastomers (e.g., the KratonTM family) and unvulcanized rubbers (e.g., natural rubber, styrene-butadiene rubber) can be used. TPUs may be used but suffer from relatively poor adhesion to the non-polar butyl. SIBS and butyl are typically light yellow in color, presumably due to slight oxidation. (This does not affect the physical properties of the materials.) We employed a laboratory press to prepare films in our detailed study [7] but such equipment may not be widely available. As an affordable and convenient alternative, films of SIBS, butyl and bilayers can be simply prepared using a T-shirt press. Empirically, conditions have been established for the pressing of films of acceptable quality using the T-shirt press. We found success in making demonstration quality films using a Signature PRO 12″ x 15″ Swing Away Heat Press with SurePressure manufactured by Heat Press Nation (HPN).
Butyl is well above its Tg (ca. -60oC) at room temperature, although heating is needed to decrease its viscosity and allow film formation. SIBS has similar material as its center block, but in this case heating to above the Tg of the polystyrene domains (ca. 100oC) is needed for the material to flow. We suggest reaching about 160oC for good coalescence of pellets of SIBS. (Poor coalescence is evident if films are seen to contain numerous internal boundaries.)
Summarized in Table 1 is all important material-specific information. In addition, a template laboratory procedure including pictures and detailed steps to aid in replication has been included in the Supplemental Information. First the press was preheated to the desired temperature for the material in question. While warming, the sample packet was prepared. Material was placed evenly in a small circle/oval on a piece of Teflon coated foil in a shim stock die of ~0.40 mm. It should be noted that the butyl is typically in slab form and needs to be cut into chunks of roughly 1 cm tall, while the other pellets can be measured using a paper cup. This was then covered by another piece of Teflon foil and sandwiched by two thin aluminum plates for maintaining flatness. The desired pressure and cycle time were then set on the unit using a rotating wheel and a digital controller. Once everything is at temperature the packet was loaded into the press and closed. If materials required times greater than allowed on the unit, multiple cycles were run. This step is critical to help ensure good quality films without pellet boundaries.
However, certain materials require a bit of mixing to get better quality films. To achieve this a kneading step is introduced where the film is removed cut into smaller pieces (typically in half) and then restacked and pressed. This helps with polymer flow and removing trapped air in samples. The samples were allowed to air cool for about 2 minutes prior to removing them from the film and inspecting them. This procedure generated single material films ranging from 1 – 3 mm thick depending on the material and the conditions (with longer times and higher pressures leading to thinner films). Once the individual films are formed to a desirable quality, a bilayer can be created. Simply take the two material films stack them and press again following the details found in Table 1 below.
Table 1- A summary of all material specific parameters can be found here. It should be noted that the pressure values below are not direct measurements rather that of a rotational counter that adjusts the moving platen height. This indirectly controls the pressure and was targeted through trial and error.
| SIBS 102T | SIBS 103T | Butyl 268 | Multi-Layer | |
|---|---|---|---|---|
| Mass | ~20 g (1/4 paper cup) | ~20 g (1/4 paper cup) | ~20 g (~1 cm tall chunks) | |
| Time (Cycles) | 25 – 33 min (1.5 – 2) | 66.6 min (4) | 16.6 min (1) | 16.6 min (1) |
| Kneading (timing) | No | Yes (after 33.3 min) | Yes (after 7 min) | No |
| Temperature | 225 °C | 225 °C | 135 °C | 135 °C |
| Pressure (unitless) | 110-130 | 110-130 | 120 (130 after 7min) | 120-130 |
It is worthwhile to first examine the behavior of strips of SIBS vs. butyl, say about 4 cm long and 0.5 cm wide. Stretching of a SIBS strip by 3x and immediate release of tension reveals a familiar behavior that is comparable to that of a common rubber band, including an audible ‘snap.’ Figure 4a is a good analogy for the behavior. Similar stretching of a butyl strip with rapid release of tension will show immediate retraction and snap. However, unlike the SIBS strip, the behavior of the butyl strip changes rather quickly if held in tension for several seconds or more. This can be understood by considering Figure 2a, the Maxwell model. With a rapid stretch-release sequence, the dashpot cannot respond at that timescale and the spring dominates. Since the butyl is unvulcanized, at times longer than a second or so the dashpot comes into play and the polymer will stress-relax due to slow net flow of chains past each other. Therefore, release of tension will not lead to full recovery of initial dimensions. Partial recovery will occur as the result of entanglements, the extent of recovery being inversely roughly proportional to the time held under tension. Prolonged holds (> 10 seconds or so) under tension will typically result in rapid stress relaxation and eventual rupture. The stage is now set for observations with bilayers.
It is suggested to cut a bilayer into a strip at least about 5 cm long. Stretch the sample manually to an extension of about 3x, and hold for 5 or so seconds and then release the tension. The bilayer should immediately bend, and then slowly relax. This phenomenon can be understood with reference to Figure 4b.
Figure 6. Schematics [7] showing a cut out from (a) an interwoven mesh of
butyl and SIBS (poly(styrene-b-isobutylene-b-styrene)) that forms the two-segment alternating bilayer strip and (b) a bilayer sheet that forms the bilayer cross, curling into a grasper following tensioning and release. Butyl is shown in light grey and SIBS is shown in darker grey.
Options for bilayer design beyond that of simple strip can be considered (Figure 6). An example is a cross pattern cut from a bilayer film, wherein tension across each of the four arms followed by release leads to an initial claw-shaped configuration that relaxes back to the planar cross. It is possible to grip, for example, a piece of foam and carry it away from its original location, followed by release of the foam at a point where the arm relaxation loosens the grip. An interesting aspect of this simple system is that only one actuation step is needed, namely the stretch. Release does not require a second stimulus, with advantage taken of relaxation of the bilayer arms. Another example is a strip with alternating butyl/SIBS sections (Figure 6). Here, stretch and release leads to multi-segment curvature and a wave-like structure that eventually relaxes. We encourage students’ creativity in designing and testing other geometries.
Rather simple polymeric bilayer constructs have been offered as examples to observe and appreciate viscoelasticity, and connections were made to common mechanical models used to describe viscoelastic behavior [10]. These examples complement others [11] and share a common educational goal about relating visual observations to an understanding molecular-level phenomena in polymeric materials.
We encourage others to build on the concepts discussed, and to share them through X (formerly Twitter) @cwrumacro with #visual viscoelasticity. Observations with new polymer combinations and multi-component configurations would be most welcome.
Support via an NSF Partnership for International Research and Education (PIRE) grant (NSF-1743475) and the DEVCOM Chemical and Biological Center is gratefully acknowledged. We thank Emily Hromi, Studio Hromi LLC, for the graphics in Figures 4a and 4b. We thank Kaneka and EXXON Mobil for samples of SIBS and butyl.
Zachary Baierl,¹ Andrew Ko,¹ Evan Chou,¹ Austin Mills,² Kathryn Daltorio,² and Gary E. Wnek,¹
¹Department of Macromolecular Science and Engineering
²Department of Mechanical an Aerospace Engineering
Case Western Reserve University
Cleveland, Ohio USA 44106
Step-by-Step Instructions:
(Optional) The bottom platen in the press used for this experiment was not entirely flat and had a minor bow. This is not an issue for pressing decals on clothing but can be detrimental in making a uniform film. To fill in the bow folded pieces of foil were used.
Place a piece of nonstick foil, nonstick side up, on a thin aluminum plate. This plate will serve as the exterior flat surface to help with handling and maintaining consistent films. This non-stick foil is critical for removing the thin films later!
Once done, carefully remove the packet using hot gloves and allow to air cool. This took about 2 minutes in the processing of butyl films but will take longer at higher temperatures.
Clean up the area by disposing of used materials, properly storing unused raw polymers, turning off the press and wiping down once cooled. Follow all press specific clean up and shut down instructions!
Table 1- A summary of all material specific parameters can be found here. It should be noted that the pressure values below are not direct measurements rather that of a rotational counter that adjusts the moving platen height. This indirectly controls the pressure and was targeted through trial and error.
| SIBS 102T | SIBS 103T | Butyl 268 | Multi-Layer | |
|---|---|---|---|---|
| Mass | ~20 g (1/4 paper cup) | ~20 g (1/4 paper cup) | ~20 g (~1 cm tall chunks) | |
| Time (Cycles) | 25 – 33 min (1.5 – 2) | 66.6 min (4) | 16.6 min (1) | 16.6 min (1) |
| Kneading (timing) | No | Yes (after 33.3 min) | Yes (after 7 min) | No |
| Temperature | 225 °C | 225 °C | 135 °C | 135 °C |
| Pressure (unitless) | 110-130 | 110-130 | 120 (130 after 7min) | 120-130 |