Modulus rubbery state

In addition to differences in shaping range, polymers also vary in their modulus or resistance to deformation in the rubbery state. If a polymer is to be... 

Although the transition from a solid to a liquid state at the Tm is relatively precise and occurs over a short temperature range, the transition from a glassy solid to a leathery state occurs over somewhat broader temperature ranges around Tr The modulus, or stiffness, of the polymer decreases as the temperature is increased above the Tg, and the polymer changes from a leathery to a rubbery state. 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

The elastic modulus in the rubbery state is directly related to ve. It has been proposed that the network stiffness under a mechanical solicitation depends on the functionality of the crosslinks (Duiser and... 

This approach can be illustrated by unsaturated polyesters based on an almost equimolar combination of maleate and phthalate of propylene glycol, crosslinked by styrene (45 wt%) (Mortaigne el al., 1992). Six samples differing by the prepolymer molar mass were analyzed. The chain-ends concentration, b, was determined by volumetric analysis of alcohols and acids in the initial reactive mixture. Then, the system was cured, elastic measurements were made in the rubbery state at Tg + 30° C, and the shear modulus G was plotted against chain-ends concentration (Fig. 14.7). The following relationship was obtained ... 

It is well known that the elasticity of polymer networks with constrained chains in the rubbery state is proportional to the number of elastically active chains. The statistical (topological) model of epoxy-aromatic amine networks (see Sect. 2) allows to calculate the number of elastically active chains1 and finally the equilibrium modulus of elasticity Eca,c for a network of given topological structure 9 10). The following Equation 9) was used for the calculations of E, c ... 

Here, E is the Young modulus in the rubbery state, d the density, R the gas constant, T the temperature in K, Mc the molecular weight between crosslinks, q the cross-linking density, and tp the front factor. The value of tp is close to unity. 

The number of resonant peaks that can be measured is dependent on the loss factor of the material, but, typically, there are three to five peaks. As expected, the resonant peaks appear at higher frequencies in the glassy state than in the rubbery state. From the amplitude and frequency of each measured resonant peak. Young s modulus and loss factor are determined at the corresponding frequency and temperature. By assuming Poisson s ratio of 0.5, Young s modulus is converted to shear modulus. The loss factor in extension is assumed to equal the loss factor in shear. 

Dynamic thermal mechanical analysis indicates significant broadening of glass transition temperature at or around PU/EP composition of 70/30. This is true for all three groups studied. At this composition, storage modulus showed much less steep variations with temperature during the transition from glassy to rubbery state. 

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

Based on studies of an homologous, endlihked, epoxy/amine network series, the simple theory of rubber elasticity has proved effective for determining reasonable cross-link densities from equilibria modulus measurements in the rubbery state. 

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