Modulus temperature effects

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. 

The net effect is that tackifiers raise the 7g of the blend, but because they are very low molecular weight, their only contribution to the modulus is to dilute the elastic network, thereby reducing the modulus. It is worth noting that if the rheological modifier had a 7g less than the elastomer (as for example, an added compatible oil), the blend would be plasticized, i.e. while the modulus would be reduced due to network dilution, the T also would be reduced and a PSA would not result. This general effect of tackification of an elastomer is shown in the modulus-temperature plot in Fig. 4, after the manner of Class and Chu. Chu [10] points out that the first step in formulating a PSA would be to use Eqs. 1 and 2 to formulate to a 7g/modulus window that approximates the desired PSA characteristics. Windows of 7g/modulus for a variety of PSA applications have been put forward by Carper [35]. 

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.

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.

The mechanical properties of silicate- based glasses have been extensively studied due to their widespread use as containers, reinforcing fibers, and optical fibers. Consequently, there is a wealth of information on the influence of many variables on the mechanical properties of these glasses. We shall concentrate on (a) composition and temperature effects on modulus and strength and (b) an important method of strength enhancement in glass fibers. 

Spiering et al. (1982) have developed a model where the high-spin and low-spin states of the complex are treated as hard spheres of volume and respectively and the crystal is taken as an isotropic elastic medium characterized by bulk modulus and Poisson constant. The complex is regarded as an inelastic inclusion embedded in spherical volume V. The decrease in the elastic self-energy of the incompressible sphere in an expanding crystal leads to a deviation of the high-spin fraction from the Boltzmann population. Pressure and temperature effects on spin-state transitions in Fe(II) complexes have been explained based on such models (Usha et al., 1985). 

The addition of smaller molecules such as plasticizers and the entrapment of monomers have an effect similar to that of the absorption of water. In general, the modulus temperature transition (temperature at which polymer stiffness changes abruptly with the polymer being stiffer below the T) and the Tg decrease as the amount of additive is increased. Thus the modulus temperature transition occurs at about 100 °C for PVC itself, 70 °C for PVC containing 10% dioctyl phthalate, and 20 C for PVC containing 30% dioctyl phthalate. 

Effects of Phase Segregation on Modulus. The magnitude of the modulus between as and h for 2,4-T-2P or 8 for 2,6-TDI block polyurethanes was found to highly depend upon hard-segment content. The presence of a plateau region in modulus-temperature plots has been attributed to phase segregation in block copolymers (27). The hard... 

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) ... 

Flexural Modulus-Temperature Behaviour. This is shown in Figure 4(a) for various RIM materials PU821to PU221, compared with PU401, where the effects of polyol compatibility versus incompatibility are more evident. In the compatible polyol-based series, reducing triol M (increasing crosslink density) together with increases in HB... 

Figure 4. Variation of flexural modulus with temperature (-30°C to 65°C) for the RIM PUs in Series I and II defined in Table I. Curves show the effects on flexural modulus-temperature behaviour and -30/65°C ratios of polyol composition and added fillers, (a) Polyol blend compatibility/incompatibility Key A, PU221 A, PU421 , PU521 O, PU621 , PU821 , PU401.

Figure 6.11 shows that the temperature effect on elastic modulus and relaxation time of the polymer solution was not significant. The polymer concentration was 2000 mg/L, and (o was 1.351 radians per second. The reason is that the increase in temperature increases the molecular thermal motion, but cannot change the polymer curling state within 5 to 55°C. Interestingly, the elastic modulus for both polymers and the relaxation time of HPAM 1255 peaked at 35°C. 

Temperature coefficient, 205, 206, 335, 495, 506, 509, 511, 512 Temperature factor, 303 Temperature, effect on viscosity, 633 Tensile modulus of elasticity of composite materials, 329... 

Dannenberg19 summarized the phenomena which must be explained by a theory of reinforcement. One of these is the reversed modulus-temperature dependence shown by the rubber on the addition of carbon black, and is closely linked to the observations by Oono et al.66. The modulus of crosslinked, unfilled rubber increases with temperature addition of carbon black reduces this tendency until, at sufficient concentration, the modulus-temperature gradient is reversed. This effect may be explained qualitatively by the saltation mechanism the more rapid thermal motions... 

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