Computational Materials Science of Polymers

Chapter X: Equilibrium Rubber Modulus for Polymer Networks

X.1 Calculations of the Equilibrium Modulus

To estimate the equilibrium rubbery modulus E ? and molecular mass of an linear fragment M c in the case of elastomer networks in the case of fairly sparse cross-links, the equation of the classic rubber elasticity theory is used:

(X.1)

where ? is the density of a cross-linked elastomer; R is the universal gas constant; T is absolute temperature.

Application of equation (X.1) to high-crosslinked networks, the linear fragment of which contains an extremely small number of units, down to 1 and even lower, causes a substantial divergence between the experimental and calculated values of E ?.

For equation (X.1) to be true for description of the properties of high-crosslinked networks, the so-called front-factor ? is introduced into it:

(X.2)

However, introduction of an unpredictable front-factor into equation (X.1) does not improve the situation, because, comparing the calculated and experimental values of E ?, we may only estimate this front-factor. In this connection, ref. [31] indicates an attempt to obtain a generalized correlation for estimation of E ? and M c which is true both for sparse and high-crosslinked networks.

Let us perform a detailed analysis of the influence of a great number of network cross-linked points on the equilibrium rubbery modulus. Preliminarily, it should be noted that for sparse networks, the Van-der-Waals volume of cross-linked points is extremely lower than the Van-der-Waals volume of linear fragments. That is why it may be...

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