Relaxed modulus, glass transition

Parameter Dynamic modulus Glass transition temperature Melting temperature Cross-link density Relaxation behaviour CrystaUinity, cure Dynamic modulus Glass transition temperature Creep, cure, compliance Relaxation behaviour Viscosity Gelation... 

Branched polyethylene shows a different behaviour (Fig. 7.47). At low temperatures, below the P relaxation (the glass transition of polyethylene), the behaviour is similar to that of linear polyethylene. At higher temperatures, above Tp, the modulus of the amorphous component is crystallinity-dependent. 

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. 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

The above discussion easily motivates the notion that reorientation times will become long as the liquid is cooled towards the glass transition, but it does not explain the shape of the observed relaxation function. Part of the shear viscosity in fluids is due to coupling to molecular reorientation. This effect has been studied in detail in alkane liquids26,27. At low viscosities the shear modulus can be described by... 

For polymers containing branched side chains Fig. 2.67 show the variation of the modulus E , E and the loss tangent for PDIPI and PDIBI in the temperature range under study. Two relaxations can be observed where the most prominent is the a relaxation associated to the glass transition as in the systems previously reported. Tg increases as the volume of the side chain increases. This result is in good agreement with that observed for the corresponding family of poly(methacrylate)s [242],... 

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