Rubbery state plateau

For the reactive system cured at a temperature, T higher than its maximum glass transition temperature Tgoo (= — 12°C), s Soto decreases to reach plateau values that are frequency dependent (Fig. 6.9a). As there is no vitrification, the plateau observed corresponds to the behavior of a network in a rubbery state. 

The rubbery state At approximately 30 K above the glass transition the modulus curve begins to flatten out into the plateau region C to D in the modulus interval 10 to lO Nm- and extends up to about 420 K. 

Above the 100 C, both the CTBN and epoxy phases are in their rubbery state and the presence of a broad rubbery plateau from T = 100 - 200 C confirms the existence of a crosslinked three-dimensional network for the CTBN modified epoxy materials shown in upper Figure 8. The measured values of E(t) = E (t) at T = 127 C = 400 K are tabulated in Table II and introduced into Eq. 1 with a nominal density p - 1.0 gm/cc to provide calculated values of the effective molecular weight between entanglements or crosslinks in CTBN modified epoxy resins. The values of reported in Table II for CTBN modified epoxy are seen to increase with % CTBN and lie intermediate between - 380 gm/mole for an ideal network of Epon 828 epoxy or 3400 gm/mole for an ideal CTBN network. 

Above To, the material remains in a rubbery state, and at this point " —> 0 due to oscillatory deformation is far slower than the cooperative segmental movements, and thus the internal reorganizations elastically absorb the solicitation. Thus, shows a constant value that may be related to the molecular weight between entanglements or crosslinks [42]. The influence of physical fillers may play a role in the -values during the rubbery plateau, as will be shown later. 

In the rubbery state the chains may be entangled and the plateau modulus can be used to obtain the entanglement molar mass. If Ge is the plateau modulus, the entanglement molar mass is defined by Me = Ge, where p is the density, K is the gas constant and T is the temperature. 

While in the temperature range called the rubbery plateau, the soft polymer responds instantaneously and reversibly to applied stress and tends to be Hookean. In the rubber state, the polymer approaches Hooke s law for... 

As the temperature is increased above the rubbery plateau, the linear amorphous polymer assumes a viscous state and may undergo irreversible flow, i.e., flows such that the original shape is lost. The flow of the viscous liquid may approach a Newtonian flow, i.e., its flow properties may be estimated from Newton s law for ideal liquids. 

The rubbery plateau can be "stabilised" by cross-linking, the regions of rubbery flow and liquid flow are completely suppressed if enough chemical cross-links are introduced to serve as permanent network junctions in place of the temporary chain entanglements. Crystallisation is a kind of physical cross-linking with (numerically) many junctions. It is understandable that the amorphous state is more or less "stabilised" by crystallisation, so that the transition becomes less pronounced. 

Another important point is that, when approaching Me, the tube consistency becomes weaker or in other words, the constraint release scaling law is modified and the rubbery plateau disappears whereas the steady-state compliance J decreEises. A self-consistent approach should predict that aroimd Me, the reptation modes would be gradually replaced by Rouse modes in order to describe the non entangled - entangled transition. 

An attempt has been made to describe the particular stress-optical behaviour observed close to Tg. The idea was to associate the entropic part of the stress with relaxation times corresponding roughly to the rubbery plateau and the terminal zone (see Fig. 12), whereas the non-entropic part is assumed to be related to shorter time relaxation phenomena (glass transition and glassy state). This approach is similar to that proposed by Inoue et al. [34] who considered two contributions to the stress with different associated stress-optical coefficients. 

Instantaneously deformed high molar mass polymer melts (long polymer chains in their liquid state) behave at intermediate times as networks with well-defined values of shear modulus, called the plateau modulus Ge, which is independent of molar mass for long-chain polymers. This rubbery plateau is seen for all polymer melts with... 

The onset of the Tg is near 175°C. This composite, which is 45° carbon-fiber-reinforced, shows a dynamic storage modulus of the epoxy matrix in the glassy-state of ca. 15 GPa. At the onset of the glass-to-rubber transition (see Figure 6), the modulus drops gradually from 15 GPa (175°C) to about 3 GPa (300°C) as the rubbery plateau is reached. 

Rubbery flow After the rubbery plateau the modulus again decreases from lO to 10 Nm in the section D to E. The effect of applied stress to a polymer in states (3) and (5) is shown in Figure 13.1(c), where there is instantaneous elastic response followed by a region of flow. 

Above the glass transition lies the rubbery plateau region, region 3. The equations of state for rubber elasticity (see Section 1.5.4) apply here if the material is crosslinked, these equations may apply up to the decomposition temperature (see dashed line. Figure 1.12). 

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