Temperature dependence of modulus

Most polymers have very strong temperature dependence of modulus, especially so when they are close to a relaxation, so that small changes in temperature during an experiment... 

Fig. 15. Temperature dependence of modulus at 25 % elongation for unfilled ( ) and filled ( , O) cured, random poly(dimethylsiloxane/methylphenyl)siloxane copolymer containing approximately 90 mol% dimediyl-, 10 mol% methylphenyl-, and 0.3 mol% methylvinyl- units [45, 46] ( ) without filler, filled by ( ) hydrophobic Aeiosii (300 m g ) and (O) hydrophilic Aerosil (60 m g ) the weight ratio filler/eiastomer is 30 100 die samples are cured at 400 K with 2 wt% of dicumyl peroxide in a presence of a platinum catalyst...

The temperature dependence of modulus data can be quite accurately described using an Arrhenius equation with the concept of time-temperature equivalence. An equivalent time, t may thus be deduced for a process at an absolute temperature, T, which occurs at t for an original temperature, Tq, such that ... 

Although both DTUL at 0.45 and 1.8 MPa are arbitrarily defined reference temperatures, they are mistakenly used as an indicator of the maximum-use temperature or continuous-use temperature of the plastic material. Limitations of DTUL in describing the temperature dependence of modulus is discussed extensively by Sepe and Nunneiy. Similarly, notched impact strength is often used in the industry as a differentiating criteria among materials for toughness. Notched impact... 

M. Sepe, The Usefulness of HDT and a Better Alternative to Describe the Temperature Dependence of Modulus, SAE Tech. Paper 1999M-221, Society of Automotive Engineers International Congress and Exposition, Detroit, Michigan, March 1-4, 1999. 

The horizontal shift factor reflects the temperature dependence of relaxation time, and the vertical shift factor reflects the temperature dependence of modulus. 

Figure 6.4 Temperature dependence of modulus in a t pical polymer...

Figure 9.7 Temperature dependence of modulus and loss for a linear amorphous...

Fig. 12 Temperature dependence of modulus/concentration ratio (G/c ) of gelatin gels at various concentrations.

In calculation the authors of the model assume that the cube material possesses the complex modulus EX and mechanical loss tangent tg dA which are functions of temperature T. The layer of thickness d is composed of material characterized by a complex modulus Eg = f(T + AT) and tg <5B = f(T + AT). The temperature dependences of Eg and tg SB are similar to those of EX and tg <5A, but are shifted towards higher or lower temperatures by a preset value AT which is equivalent to the change of the glass transition point. By prescibing the structural parameters a and d one simulates the dimensions of the inclusions and the interlayers, and by varying AT one can imitate the relationship between their respective mechanical parameters. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

Temperature dependence of the elastic modulus of the plastic liner. 

Figure 5. From left to right temperature dependence of the storage modulus at 0.5 Hz, and of the reduced stress, ( 1.03). Key , PDMS-B1 O, PDMS-B2 X, PDMS-B6 A, PDMS-B7.

The modulus-time or modulus-frequency relationship (or, graphically, the corresponding curve) at a fixed Temperature is basic to an understanding of the mechanical properties of polymers. Either can be converted directly to the other. By combining one.of these relations (curves) with a second major response curve or description which gives the temperature dependence of these time-dependent curves, one can cither predict much of the response of a given polymer under widely varying conditions or make rather... 

The temperature dependence of the compliance and the stress relaxation modulus of crystalline polymers well above Tf is greater than that of cross-linked polymers, but in the glass-to-rubber transition region the temperature dependence is less than for an amorphous polymer. A factor in this large temperature dependence at T >> TK is the decrease in the degree of Crystallinity with temperature. Other factors arc the reciystallization of strained crystallites ipto unstrained ones and the rotation of crystallites to relieve the applied stress (38). All of these effects occur more rapidly as the temperature is raised. 

The temperature dependences of the isothermal elastic moduli of aluminium are given in Figure 5.2 [10]. Here the dashed lines represent extrapolations for T> 7fus. Tallon and Wolfenden found that the shear modulus of A1 would vanish at T = 1.677fus and interpreted this as the upper limit for the onset of instability of metastable superheated aluminium [10]. Experimental observations of the extent of superheating typically give 1.1 Tfus as the maximum temperature where a crystalline metallic element can be retained as a metastable state [11], This is considerably lower than the instability limits predicted from the thermodynamic arguments above. 

Figure 10.5 Temperature dependence of storage modulus ( ) and mechanical...

Figure 1. Temperature dependence of dynamic modulus and loss tangent (11 Hz) of monomer I cured for 7 days at 280°C.

Finally, it behaves like a liquid provided the chain length is not too long. Just around T some physical properties change distinctively such as the specific volume, the expansion coefficient, the specific heat, the elastic modulus, and the dielectric constant. Determination of the temperature dependence of these quantities can thus be used to determine Tg. 

Softening as a result of micro-Brownian motion occurs in amorphous and crystalline polymers, even if they are crosslinked. However, there are characteristic differences in the temperature-dependence of mechanical properties like hardness, elastic modulus, or mechanic strength when different classes of polymers change into the molten state. In amorphous, non-crosslinked polymers, raise of temperature to values above results in a decrease of viscosity until the material starts to flow. Parallel to this softening the elastic modulus and the strength decrease (see Fig. 1.9). 

Free Volume Versus Configurational Entropy Descriptions of Glass Formation Isothermal Compressibility, Specific Volume, Shear Modulus, and Jamming Influence of Side Group Size on Glass Formation Temperature Dependence of Structural Relaxation Times Influence of Pressure on Glass Formation... 

In addition to the temperature dependence of the properties such as strength and modulus, which we will discuss individually for each material class, there are two fundamental topics that are often described in the context of heat transfer properties or thermodynamics of materials—for example, thermal conductivity or specific heat—but are related more to mechanical properties because they involve dimensional changes. These two properties, thermoelasticity and thermal expansion, are closely related, but will be described separately. 

---