Modulus vs. Temperature Behavior

The variation of modulus with temperature can be determined from relaxation tests conducted at different temperatures. In a relaxation test (Fig. 3.14) conducted at a constant temperature, the ratio of stress to strain at a given instant in time of 10 seconds, one minute, or another suitable time, is identified as the ten second modulus, E(10), or one minute modulus, E(l), etc. 

The variation of the 10 second relaxation modulus with temperature for 

Two very important temperatures are indicated in Fig. 3.15 and are the melt temperature (or first order transition temperature), T j and the glass transition (or second order transition temperature) Tg. The T and Tg can only be determined approximately from isochronous modulus-temperature data similar to that given in Fig. 3.15. Often, manufacturers specification 

In Fig. 3.17, both occupied and free volume regions are indicated. The occupied volume is the portion of polymer containing molecular mass and the free volume represents the region within the polymer that is not occupied by molecular mass. As a rule of thumb, the free volume at the Tg is approximately 2.5% of the total volume. The variation of free volume 

---

Figure 1-2. Schematic of the modulus vs. temperature behavior for a rubber and a plastic over a broad temperature range.

Figure 4-2. Shear modulus vs. temperature behavior for two polycarbonate samples of different molecular weights, along with the response of a partially crystallized sample. (See Chapter 5 for additional discussion.) [Adapted from J. P. Mercier, J. J. Aklonis, M. Litt and A. V. Tobolsky, J. Appl. Polym. Sci. 9, 447-459 (1965). Copyright 1965 Wiley Periodicals, Inc.,...

The physical properties of the acid- and ion-containing polymers are quite interesting. The storage moduli vs. temperature behavior (Figure 8) was determined by dynamic mechanical thermal analysis (DMTA) for the PS-PIBMA diblock precursor, the polystyrene diblock ionomer and the poly(styrene)-b-poly(isobutyl methacrylate-co-methacrylic acid) diblock. The last two samples were obtained by the KC>2 hydrolysis approach. It is important to note that these three curves are offset for clarity, i.e. the modulus of the precursor is not necessarily higher than the ionomer. In particular, one should note the same Tg of the polystyrene block before and after ionomer formation, and the extension of the rubbery plateau past 200°C. In contrast, flow occurred in... 

For a polymer where crystallinity dominates its relaxation behavior, the situation is quite different. Figure 4-3 shows the 10-second modulus vs. temperature curve for such a crystalline polymer, polyethylene (PE). Included also in this figure is the modulus-temperature curve for polyvinyl chloride... 

In the same work, the damping behavior of those three component LIPNs was evaluated from the integrals of the linear loss shear modulus vs. temperature (loss area, LA) and linear tan 8 vs. temperature (tan 8 area, TA) curves measured by... 

Fig. 1 Four types of SMPs (dual-shape effect) depicted as a function of their dynamic thermomechanical behavior. Plotted is the tensile storage modulus vs temperature as measured using a smtdl oscillatory deformation at 1 Hz for (a) Cat. A-I, chemically crosslinked amorphous polymer network (7, = Tg) (b) Cat. A-II, chemically crosslinked semicrystalline polymer networks (Ttrans = 7m) (c) Cat. B-I, physically crosslinked thermoplastic with r,ra,K = 7g and (d) Cat. B-II, physically crosslinked thermoplastic (Tlrans = Tm). Taken from ref [5], Copyright 2007. Reproduced by permission of the Roytd Society of Chemistry, http //dx.doi.org/10.1039/b615954k...

Pig. 45. Schematic diagram showing the effects of cross-linking on modulus and damping (loss tangent) vs temperature behavior at Tg. 

Name the five regions of viscoelastic behavior of a polymer and give a sketch of the 10 second modulus vs. temperature for thermoplastic (amorphous and crystalline) and thermoset polymers. 

Young s Modulus. Young s moduli, E, for several resins are plotted vs. temperature in Fig. 7. Young s moduli were determined from stress-strain diagrams. At 4K, their values are within 10%. Therefore, the low-temperature values of E do not depend markedly on the detailed chemical structure. It must be emphasized that epoxy resins are energy-elastic and have a nearly linear stress-strain behavior to fracture at low temperatures. No rate dependence was found over several decades. This is not true for many high polymers, such as polyethylene (PE), which are not cross-linked. PE behaves viscoelastically, even at 4 K [%... 

In the following, we expect an Arrhenius-like temperature behavior for highly filled rubbers that is typically fotmd for polymers in the glassy state. Therefore, we measure—far above the polymer bulk glass transition temperature—the modulus G for small deformation amplitudes (0.2% in our case). This is depicted schematically in Fig. 36.10. One obtains a straight line of slope E /R by plotting log G (T) (or in the tensile mode log E (T)) vs. 1/T well above the bulk... 

To illustrate the effect of temperature on mechanical properties, it is sometimes preferable to plot the property vs. temperature for constant values of time. For example, data of the type shown in Fig. 18.21 may be cross-plotted as (10) (the 10-second relaxation modulus) vs. T, Such a plot is given in Fig. 18.23 for several polystyrene samples," The five regions of viscoelastic behavior are evident in the linear, amorphous (atactic) samples (A) and (C) along with the effect of molecular weight in the flow region. The drop in modulus in the vicinity of Tg (100°C) is dearly seen. The crystalline (isotactic) sample maintains a fairly high modulus all the way up to (a 235 "C). Given values of one can convert data in the form vs, t at constant T (a master curve) to vs. T at constant t and vice versa. 

Figure 3 shows the stress vs. strain behavior of the 310,000 M polymer at an applied shear rate, y, of 0.053 sec at various temperatures. The initial portion of each curve is essentially a straight line the slope of which gives the shear rate dependent modulus, of the melt. Then there... 

The tensile modulus E is not a constant when o varies, and it also depends on temperature T. For these reasons, curves showing the dependence of a vs. e at constant temperatures or of E vs. T are used for the understanding of polymer behavior under mechanical stress. The value of E (in dyn cm or N m ) is usually given at polymer break. 

Tobushi et al. (2001) presented an empirical model based on the observation of the thermo-mechanical behavior of shape memoiy polymers (SMPs). In the model, the modulus of the SMPs was considered to linearly decrease with the temperature increase in a narrow region around T (T - T < T < T + T ). The stress vs strain profiles in shape memorization were predicted based on a nonlinear visco-elastic equation. This model mainly took account of the modulus variation above and below T, but noted no further microscopic changes in the shape memorization (Tobushi et al., 2001). 

---