Glass transition cross-linked polymers

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.

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. 

Sonic absorption on the other hand is - for linear polymers - a typical constitutive property, dependent of temperature and frequency, for which no additivity techniques are available. For cross-linked polymers the integrated loss modulus-temperature function (the "loss area") in the glass-rubber transition zone shows additive properties. 

The highest sonic damping is obtained in transition zones. The glass transition can be used for this purpose if cross-linked polymers are applied, with a rubbery solid state until far above Tg. Very interesting work in this field was done by Sperling and his coworkers (1987,1988) who studied the damping behaviour of homopolymers, statistical copolymers and interpenetrating networks (IPNs) of polyacrylics, polyvinyls and polystyrenes. 

Using results such as these, c.ie can predict the Tg of any polymer for which the group contributions are known. The glass transition temperature for polydimethylsiloxane, for example, is Tg = (1/2) 20 + (1/2) 280 = 150 K = -123 0. The approach was originally applied to linear polymers but has been extended to cross-linked polymers as well (24) ... 

We have previously stressed that network formation rapidly increases viscosity and causes gelation. Cross linking after that point increases the apparent glass transition temperature. Figure 11 illustrates the effect of degree of cross linking on the dynamic modulus of a thermoplastic and a cross-linked polymer. The point at which modulus drops off rapidly is approximately the glass transition temperature. 

Their work points out that the change in glass transition of a cross-linked polymer is due to the combined eflFects of cross linking (AT )p and the structure of the cross-linking molecules (aT ). ... 

Beloshenko, V. A. Kozlov, G. V. Lipatov, Yu.S. Glass transition mechanism of cross-linked polymers. Physics of Solid Body, 1994,36(10), 2903-2906. 

Weakly cross-linked polymers are rubberlike above their glass transition temperatures. Such rubbers simultaneously exhibit characteristic properties of solids, liquids, and gases. Like solids, they have dimensional stability and behave as Hookean bodies for small deformations. On the other hand, they possess similar expansion coefficients and moduli of elasticity as liquids. Just as the pressures of compressed gases increase with increasing temperature, the stresses for rubbers also increase (Figure 11-3). In contrast, the stresses increase with decreasing temperature below the glass transition temperature. 

Depending on their structure and factors such as temperature and strain rate, polymers may exhibit brittle or ductile failure (Figure 2.4). Highly cross-linked polymers well below their glass transition are often brittle, with maximum elongation of the order of 1-4%. Semi-ciystaUine polymers are also brittle when... 

Further in many calculating equations, there are glass transition temperature and thermal expansion s coefficient. For cross-linked polymers glass transition temperature (rg,K)[2]... 

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