Viscoelastic materials, like plastics, consist of long fiber-like particles. In case of plastics the fibers are formed by the macromolecules that are entangled with each other. Due to this structure, plastics can store elastic energy, at least temporarily.
Depending on the temperature these macromolecules can be stiff or flexible, causing the polymer to be in the glass phase or in the rubber phase. At even higher temperatures the macromolecules are able to move (reptate) into other positions. By then the plastic behaves like a fluid. It is in the melt phase.
In the previous chapters we have explained how the macroscopic behavior of the plastics (glass, rubber and melt phase, stress relaxation, creep, etcetera) are related to the molecular properties. This is good for a fundamental understanding of the physical properties of polymers. However, it may be difficult to extrapolate this knowledge into day-to-day practice for polymer products.
It is therefore common practice to visualize the plastic as a combination of springs and dashpots. The springs describe the elastic behavior of the plastic; the dashpots describe the viscous behavior of the plastic. Such a spring – dashpot representation of a polymer is shown in the figure below.
Spring 1 is a spring with a high stiffness. The spring modulus is the glass modulus. It represents the glass stress in the polymer. Dashpot 1 will change its length after a relatively short time: the segmental rotation time. It represents the viscous dissipation due to rotation of the chain segments. Spring 2 is a spring with a low stiffness. The spring modulus is the rubber modulus, which is about 1000 times less than the glass modulus. It represents the rubber stress in the polymer. Dashpot 2 will change its length after a relatively long time: the reptation time. It represents the viscous dissipation due to reptation of the macromolecules.
The effects of temperature, stress and aging on the polymer follow from the chain segment rotation time and the molecular reptation time. Be aware that the model with dashpots and springs provides no molecular basis for the viscoelastic response. It is only useful for investigating the macroscopic behavior of the polymer.
Some examples
Glass phase
Both the rotation time and the reptation time are large. Dashpots 1 and 2 are fully blocked. The stiffness of the system is that of the sum of both springs. The stiffness of spring 1, which represents the glass stress, is about 1000 times higher than that of spring 2. Therefor the glass stress is the most important stress in the glass phase.
Rubber phase
The rotation time is low (less than 1 second) but the reptation time is still large. Therefore dashpot 1 can move but dashpot 2 is still blocked. Spring 1, representing the glass stress becomes unloaded. Upon deformation the stress in the system will be represented by that of spring 2: the rubber stress.
Melt phase
Both the rotation time and the reptation time are low now. Both dashpot 1 and 2 can move. Any stress generated by deformation of the system (spring 1 and spring 2) will reduce in time due to the moving dashpots (stress relaxation). Since the segmental rotation time is much less than the reptation time, the stress of spring 1 will always be zero. The stress in the system is controlled by that of spring 2. The typical time with which the stress reduces is controlled by dashpot 2 (reptation time).
Viscous flow of melt
The speed of deformation of the plastic is high. Due to the high temperature in the plastic dashpots 1 and 2 are unblocked. Yet, dashpot 2 (reptation) still creates some resistance as long as the speed of deformation of the polymer (spring 2) exceeds that of dashpot 2. The rubber stress in the plastic will increase. The segmental rotation time (dashpot 1) is so low that the glass stress (spring 1) will remain zero.
Upon ongoing deformation, the rubber stress (spring 2) will increase. Due to the increasing stress the reptation time (dashpot 2) reduces. It becomes increasingly difficult to create additional stress. Eventually the speed of dashpot 2 will match the speed of deformation. The stress will now remain constant during deformation. The ratio between stress and speed of deformation is called viscosity.
Creep
Creep of the polymer is usually measured in the glass phase. A constant stress is applied to the product. Dashpots 1 and 2 are fully blocked on short time scale. Immediately after applying the stress spring 1 will be deformed. The initial deformation is elastic and fully recoverable.
The segmental rotation time (dashpot 1) is very long but not infinite. That means that dashpot 1 can very slowly move when waiting long enough. The deformation of the product now slowly increases which is called creep.
During the creep process spring 2, representing the rubber stress, is slowly extended while daspot2 (reptation) is fully blocked. Due to this the rubber stress in the product (spring 2) will slowly increase, counteracting the externally applied stress. This slows down the speed of the creep process.
On removing the stress spring 1 becomes undeformed immediately. The total deformation is partially undone. This part is called elastic recovery. The plastic is still deformed and the rubber stress present (spring 2) will slowly reduce the deformation by stimulating segmental rotation (dashpot 1). Due to the low level of the rubber stress a full recovery is impossible during the time span available.
Yield stress
The yield stress is usually important for the polymer in the glass phase. Both the rotation time and the reptation time are large. Dashpots 1 and 2 are fully blocked. The deformation of the product is continuously increased. Upon increasing the deformation, the stress in spring 1 increases (dashpot 1). The stress in spring 2 can be neglected. Due to the increasing stress the segmental rotation time will reduce. Once the segmental rotation time becomes less than 1 second the segments start to rotate and dashpot 1 starts moving. From this moment on spring 1 cannot create additional stress anymore. The stress remains constant and equals the yield stress.
Summary
- The viscoelastic behavior of a polymer can be represented by a mechanical model with two springs and two dashpots.
- The model uses two spring – dashpot combinations in a parallel set-up. One spring – dashpot combination is for the glass stress and the rotation time of the chain segments, the other is for the rubber stress and the reptation time of the macromolecules.
- With the mechanical model it is easy to understand the macroscopic relation between strain, stress and time in a polymer.
- The mechanical analogue is not suited for understanding the relation between the molecular configuration and the viscoelastic properties of a polymer.