Hyperelastic state

The investigation of the temperature dependence of dielectric characteristics of these block-copolysulfonarilates showed that the permittivity in the interval 20-250°C is stable. When higher than this temperature its increase is seen, which is explained by the transition to a hyperelastic state. 

For cross-linked polymers in hyperelastic state thermal expansion s coef Ctient (, K or degree ) is expressed from Simkhi Boyer s equation ... 

For concerned experimental models hyperelastic state s constant (A, K/MPa) can be written in the next expression [3] ... 

Expression, determined for (hyperelastic state), has next form ... 

As electromagnetic anisotropy, appearing in strain of polymers in hyperelastic state, is... 

Expression a for densely cross-linked polymers in glassy state is analogos to the same, derived for densely cross-linked polymers in hyperelastic state, but in the formula is used thermal expansion s coefOcient of glassy state... 

Operator in glassy and hyperelastic states of cross-linked polymers is equal to from 0 to 1, respectively, and in transition region between these conditions from 0 to 1. Therefore Equations (1) and (2) reproduce change of concerned cross-linked polymers hyperelastic properties in all their physical states in hyperelastic, where is being momentary a-process, shear pliability s relaxation operator is equal to equilibrium shear pliability in glassy, where is only local conformational mobility of polymeric mesh s cross-site chains, shear phabihty s relaxation operator is equal to shear pliability of glassy state in transition region between these states, where both... 

It was proved experimentally, that expressions (4) and (5) are effective only for hyperelastic state of cross-linked polymers. To describe change of strain electromagnetic anisotropy in all cross-linked polymers physical states will consider strain electromagnetic susceptibility s C (MPa" ) and electromagnetic susceptibility elastic coefficient s relaxation operators. Suppose that they are submitted by such appropriateness, by which equilibrium properties in equation (5)... 

Hyperelastic State s Constant and Electromagnetic Susceptibility s Equilibrium Coefficient... 

TABLE 1 Values of glass transition temperature, hyperelastic state constant, electromagnetic susceptibility equilibrium elastic coefficient, weighting coefficients and width of mode for the used experimental objects. 

Calculation K for densely cross-linked polymers in hyperelastic state will make in the network of the same approach, that in [3], Average values of strain region s worth... 

Glassy and hyperelastic states of tightly sewn polymers are determined by values of operator - N,a 0 and 1, respectively, and a transition region between these states by values in interval of 0-1. This make it possible to describe Equations (1)(4) tensor of deformation and phability of dense polymer meshes in all physical states. So, in hyperelastic state cooperative (X -transition is momentary and relaxation operator of... 

Researched experiment results showed suf Cbiently high accuracy of accounts with the use of Equation (5). It was shown that for all experimental objects hyperelastic state constant does not depend on temperature within error of experimental data (Table ), though it is values rise with increase of hardeners molar ratio, in other words with growth of polymerization number average degree of cross-site chains and synchronous decrease of mesh points concentration. 

The a-relaxation times spectrums properties were considered with the help of least squares method by isothermal creep curves for several temperature values, which lie in transition region between glassy and hyperelastic states. 

FIGURE 1 Dependence of a-relaxation average times decimal logarithm on temperature in region between glassy and hyperelastic states for model with structure x =. ... 

TABLE 1 Experimental values of glass transition temperature and hyperelastic state constant weighting coefficient and a-mode width. 

Thereby, for chosen experimental objects were determined unknown parameters of developed mathematical model hyperelastic state constant, weighting coefficient and relaxation spectmm properties. Prediction results of thermomechanical curves trend successfully demonstrated prediction abihty of introduced mathematical description of thick cross-linked polymers viscoelastic pliability in all their physical states (Figure). 

Cross-linked matrix Hyperelastic states Relaxation spectrum Strain tensor a-Relaxation... 

It is possible to calculate the coef Ciient of thermal expansion in hyperelastic state according to the Simkhi-Boyer s equation for cross-linked polymers ... 

A theoretical value of the hyperelastic state s constant for experimental objects estimate according to the Equation [3] ... 

Values Fand, defined according to Equations (10) and (11) are given in Table 2. TA B L E 2 The Hyperelastic state s constant and front factor (Theoretical and experimental values)... 

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