Additive moduli for crosslinked epoxies

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Abstract
Ultrasonic measurements were made on a series of eight crosslinked polyepoxides over the temperature range from 0 to 60°C at a frequency of 2 MHz. From these measurements the bulk (K) and shear (G) moduli were calculated. These data were then analyzed in terms of molecular component properties. Proceeding by analogy with Rao's rule for liquids, the authors found that K is not an additive property but the function U = V(K/ρ)1/2γ is an additive property. Here V is molar volume, ρ is the density, and γ is the Gruneisen parameter (for interchain vibrations). A similar relation was found to hold for shear modulus. In particular, G is not an additive property but W = V(G/ρ)1/2g is an additive property, where g = (1/2α) (∂ InG/∂T)p – 1/2 is the shear analog of the Gruneisen parameter. Using U and W, calculations were made of K and G as functions of temperature for the eight epoxies. These results agree with the measured values within the experimental uncertainty of the measurements.

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