Amorphous polymer, viscoelastic response

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

With polymers, complications may potentially arise due to the material viscoelastic response. For glassy amorphous polymers tested far below their glass transition temperature, such viscoelastic effects were not found, however, to induce a significant departure from this theoretical prediction of the boundary between partial slip and gross slip conditions [56]. 

The constitutive model makes use of the decomposition of the rate of deformation D into an elastic, De, and a plastic part, Dp, as D = De + Dp. Prior to yielding, no plasticity takes place and Dp = 0. In this regime, most amorphous polymers exhibit viscoelastic effects, but these are neglected here since we are primarily interested in those of the bulk plasticity. Assuming the elastic strains and the temperature differences (relative to a reference temperature T0) remain small, the thermoelastic part of the response is expressed by the hypoelastic law... 

The situation is somewhat similar in the case of polyvinyl chloride (PVC). PVC has a far lower degree of crystallinity than polyethylene so that the viscoelastic response of PVC might be expected to approximate more closely that of an amorphous polymer than does polyethylene. Figure 4-3 indicates that... 

It has been repeatedly emphasized throughout this book that the glass transition in amorphous polymers is accompanied by profound changes in their viscoelastic response. Thus the stress relaxation modulus commonly decreases... 

In spite of these complications, the viscoelastic response of an amorphous polymer to small stresses turns out to be a relatively simple subject because of two helpful features (1) the behavior is linear in the stress, which permits the application of the powerful superposition principle and (2) the behavior often follows a time-temperature equivalence principle, which permits the rapid viscoelastic response at high temperatures and the slow response at low temperatures to be condensed in a single master curve. 

The time-temperature equivalence principle makes it possible to predict the viscoelastic properties of an amorphous polymer at one temperature from measurements made at other temperatures. The major effect of a temperature increase is to increase the rates of the various modes of retarded conformational elastic response, that is, to reduce the retarding viscosity values in the spring-dashpot model. This appears as a shift of the creep function along the log t scale to shorter times. A secondary effect of increasing temperature is to increase the elastic moduli slightly because an equilibrium conformational modulus tends to be proportional to the absolute temperature (13). 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

This has the same form as Eq. (7.1) the renamed constants are a Young s modulus , and a viscosity 17. It is not possible to directly link these constants to the modulus of the crystalline phase and the viscosity of the amorphous inter-layers in a semi-crystalline polymer. Hence, the Voigt model is an aid to understanding creep, and relating it to other viscoelastic responses, rather than a model of microstructural deformation. 

The occurrence of significant crystallinity in a polymer sample is of considraable consequence to a materials scientist. The properties of the sample — the density, optical clarity, modulus, and general mechanical response — all change dramatically when crystallites are present, and the polymer is no longer subject to the rules of linear viscoelasticity, which apply to amorphous polymers as outlined in Chapter 13. Howcvct, a polymer sample is rarely completely crystalline, and the properties also depend on the amonnt of crystalline order. 

The mechanical properties are dependent on both the chemical and physical nature of the polymer and the environment in which it is used. For amorphous polymers, the principles of linear viscoelasticity apply, but these are no longer valid for a semicrystalline polymer. The mechanical response of a polymer is profoundly influenced by the degree of crystallinity in the sample. 

Next we note that there are two physieally different sources of temperature and pressure dependence of the elastic constants of polymers. One, in common with that exhibited by all inorganic crystals, arises from anharmonic effects in the interatomic or intermolecular interactions. The second is due to the temperature-assisted reversible shear and volumetric relaxations under stress that are particularly prominent in glassy polymers or in the amorphous components of semi-crystalline polymers. The latter are characterized by dynamic relaxation spectra incorporating specific features for different polymers that play a central role in their linear viscoelastic response, which we discuss in more detail in Chapter 5. 

The viscoelastic response of amorphous polymers at elevated temperatures is governed to a significant extent by the average molecular weight, M , the presence of any long chain branching, and the MWD [100-105]. Even the... 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

The simplest type of viscoelastic behaviour as shown by single-phase amorphous polymers is described in this article. Polymers that crystallize or form multiple phases such as blends, block copolymers, particulate or fibre-filled polymers show more complex behaviour, since each amorphous region will show its own viscoelastic response to deformation. 

Figure 3 illustrates the ideal viscoelastic behaviour for a simple amorphous polymer. It shows how the regions of rate (and temperature) independence coincide with elastic (spring) behaviour (where G G ), and regions of high rate (and temperature) dependence coincide with viscous (dashpot) response (where G G"). 

Wheat starch is composed of two components itself amylose, a linear, amorphous polymer and amylopectin, a branched, semicrystaUine polymer (10). The protein is known as gluten, also composed of two polymers, gliadin, a low-molecular-weight, soluble polymer and glutenin, a high-molecular-weight, cross-linked, elastic polymer primarily responsible for the viscoelastic properties of bread doughs. 

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