Modulus-temperature curve

Fig. 1. Modulus—temperature curve of amorphous and cross-linked acryflc polymers. To convert MPa to kg/cm, multiply by 10.

Measurement of modulus over an extensive temperature range offers more information than T alone (16). Typical modulus—temperature curves are shown in Figure 1. Assuming that the reference temperature is the transition temperature of the copolymer, then curve A of Figure 1 is that of a softer polymer and curve B is that of a harder polymer. Cross-linking of the polymer elevates and extends the mbbery plateau Htde effect on T is noted until extensive cross-linking has been introduced. In practice, cross-linking of methacryhc polymers is used to decrease thermoplasticity and solubihty and to increase residence. 

Fig. 5. Flexural modulus—temperature curves of C, polysulfone and B, polyethersulfone compared to the moduli curves of A, polyacetal D, heat-resistant...

Fig. 19. Generalized modulus—temperature curves for polymeric materials showing the high modulus glassy state, glass-transition regions for cured and uncured polymers, plateau regions for cross-linked polymers, and the dropoff in modulus for a linear polymer.

Figure 7 Effect of crystallinity on the modulus- temperature curve. The numbers on the curves are rough approximations of the percent of crystallinity. Modulus is given in dyn/cnr.

Plasticizer and Copolymerization change the glass transition temperature as discussed in Chapter 1. Plasticixers have little effect on Copolymerization can change although less strongly than 7 x. As a result, the basic modulus-temperature and modulus-time curves are shifted as shown in Figure 8 for different compositions. The shift in the modulus-temperature curve is essentially the same as the shift in TK. The shift in the modulus-time curve includes this plus the effect of any change in ()jr... 

Figure 8 Effect of plasticization or copolymerization on (A) the modulus-time and (B) modulus -temperature curves. The curves correspond to different plasticizer concentrations or to different copolymer compositions. Curve B is unplasticized homopolymer A is eithei a second homopolymer or plasticized B.

Figure 9 Modulus-temperature curves of two-phase polyblends and block polymers of widely different TK values. The numbers on the curves are rough estimates of the volume fraction of the component with the lower TK value, which is shown both as an amorphous and as a cross-linked material (dashed line). Modulus is given in dyn/cmJ.

Figure 1. Modulus-temperature curves for various plastics...

Figure /. Modulus-temperature curves for pure and plasticized (30 wt. % dioctyl phthalate) polyvinyl chloride...

For the PVN-PEO polyblends, volume changes at melting temperature (Figure 6) as well as x-ray data at room temperature (2) show that the 25% (PEO) blend is completely amorphous, and that the 50 and 75% blends contain significant amounts of amorphous PEO. Calculations based on specific volume data indicate that the crystalline part of both the 50 and 75% blends consists of PEO, whereas the amorphous part contains 46% PEO and 54% PVN. Another important result is that the unusual phenomenon of a well in the modulus temperature curves (Figure 1) was observed only for the blends which exhibit crystallinity. Based on these observations, the behavior of blends could be interpreted by postulating that the amorphous PEO forms a complex phase with PVN in the ratio of 3 to 1 monomer units (i.e., 46 wt. % PEO to 54 wt. % PVN), respectively. 

Dynamic-Mechanical Measurement. This is a very sensitive tool and has been used intensively by Nielsen (17) and by Takayanagi (18). When the damping curves from a torsion pendulum test are obtained for the parent components and for the polyblend and die results are compared, a compatible polyblend will show a damping maximum between those of the parent polymers whereas the incompatible polyblend gives two damping maxima at temperatures corresponding to those of the parent components. Dynamic mechanical measurement can also give information on the moduli of the parent polymer and the polyblend. It can be shear modulus or tensile modulus. If the modulus-temperature curve of a polyblend locates between those of the two parent polymers, the polyblend is compatible. If the modulus-temperature curve shows multiple transitions, the polyblend is incompatible. 

The temperature dependence of the relaxation modulus at 500 seconds of polycarbonate (7), polystyrene (8), and their blends (75/25, 50/50, and 25/75) was obtained from stress-relaxation experiments (Figure 4, full lines). In the modulus-temperature curves of the blends, two transition regions are generally observed in the vicinity of the glass-rubber transitions of the pure components. The inflection temperatures Ti in these transition domains are reported in Table I they are almost independent on composition. The presence of these two well-separated transitions is a confirmation of the two-phase structure of the blends, deduced from microscopic observations. 

Table I. Characteristic Parameters Deduced from the Modulus-Temperature Curves...

To apply Equation 1, the model parameters A and 0 have to be determined. They are derived from the calculated modulus-temperature curves which best fit the experimental data of Figure 4. To perform these calculations, one of the components has to be taken as the continuous phase. For the 75/25 and 50/50 blends, PC was taken as the continuous phase while for the 25/75 blend, PST was taken as this phase. This choice is based on the morphological study and the mechanical behavior reported earlier. The A and 0 values used to fit the data are reported in Table II. A fairly good agreement is found in the temperature range between 95° and 140°C. 

For amorphous thermoplastic polymers the general view of the Young modulus is shown as a function of time in Fig. 13.11. In this figure the various regions are present as they were also shown in Figs. 13.3 and 13.7. In those figures, however, the modulus is presented as a function of temperature. Formally a modulus temperature curve is obtained by measuring stress relaxation as a function of time at many different... 

It is clear that the determination of such a modulus temperature curve takes an awful lot of time. Moreover, the transitions in the glassy region are difficult to determine, because the time needed for such a transition will be very small it may be of the order of or even much faster than the time in practice to apply an instantaneous deformation. For that reason in general use is made of dynamic mechanical measurements as a function of frequency to elucidate the modulus temperature curves, in particular in the glassy region. An additional advantage is that elastic and viscous forces are separated in this kind of measurements. 

The temperature at which the damping peak occurs is not the same as that at which the discontinuous change in a thermodynamic quantity is found. The damping peak will always nearly coincide with the point of inflection of the modulus-temperature curve, whereas the conventional transition temperature is at the intersection of the two tangents... 

Sperling et al. made an important discovery, viz. that the area under the linear loss modulus-temperature curve (coined by them loss area, LA) (see Fig. 14.7) is a quantitative measure of the damping behaviour and moreover, possesses additive properties ... 

By analogy with the solubility parameter approach, the loss area, LA, for the area under the loss modulus-temperature curve in the vicinity of the glass-rubber transition is given by (7.9j... 

Fig. 11. Group contribution analysis leads to the determination of the effective area under the loss modulus-temperature curve. As in any spectroscopic experiment, background must be subtracted, and the instrument calibrated.

The damping behavior of polymers can be altered to optimize either the temperature span covered or the damping effectiveness for particular temperatures. The area under the loss modulus temperature curve tends to be constant for some polymer combination, which has been expressed by the empirical "temperature band width law" of Oberst (2) ... 

At sufficiently low temperatures a polymer will be a hard, brittle material with a modulus greater than lO N m (10 dyn/cm ). This is the glassy region. The tensile modulus is a function of the polymer temperature and is a useful guide to mechanical behavior. Figure I 1-8 shows a typical modulus-temperature curve for an amorphous polymer. 

Tg from static measurements or the maximum in the loss modulus-temperature curve. 

Figure 4-1. Schematic modulus-temperature curve showing various regions of viscoelastic behavior.

The data for the modulus-temperature curve are most often gathered in the dynamic mode at a fixed frequency of around 1 rad/s, either in shear or flex, depending on the stiffness range of the test material over the desired temperature range. See Appendix 3 of Chapter 2. 

Thus, during the experiment the sample has undergone flow, and this area of the 10-second modulus temperature curve is therefore called the flow region. 

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... 

Once again, it should be pointed out that the exact shape of the modulus-temperature curve of a crystalline polymer depends on the thermal history of the sample, particularly on the rate of cooling from the melt and annealing treatment. Two crystalline polymers are mechanically equivalent," for practical purposes, if they have the same values of Tg, Tm chain length, percentage of crystallinity, and crystalline structure. Because this is rarely the case, semicrystalline polymers exhibit a wide spectrum of properties. 

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