Application of the Theory to Vulcanizates of Natural Rubber

Abstract

Four kinds of natural rubber were used for specimens, the kinds A, B and C were cured with sulphur and the kind D was cured with peroxide. The kinds A, B and C had different initial densities of crosslinking.
The actual density, N₀ for the four samples, was obtained by using the equation of f(0)=N₀ RT (α-α^-2) and by the swelling method using the equation of Flory-Rhener.
According to the results obtained already, both the scissions of main chains and crosslink sites occurred at the same time for A, B and C, but the only main-chain scission occurred for the sample D.
The Eq. (1) was obtained for the sample D because k=0 in the Eq. (3) of
[f_t/f₀={1-2k/M₀·q_m(t)}·e^{-x/M₀·q_m(t)}+k/M₀·q_m(t)·e^{-2x/M₀·q_m(t)}]
(f_t/f₀)D=e^{-xD/M₀·q_m(t)} (1)
or
q_m(t)=-N_{0, D}ln(f_t/f₀)_D (2)
As the Eq. (3) of [f_t/f₀={1-2k/M₀·q_m(t)}·e^{-x/M₀·q_m(t)}+k/M₀·q_m(t)·e^{-2x/M₀·q_m(t)}] is applicable to the samples of A, B and C, and q_m (t) is equal to the four samples under the same condition, the Eq. (4) is established by substituting the Eq. (2) into the Eq. (3).
-N_{0, D}ln(f_t/f₀)_D=(f_t/f₀)_A-(f_t/f₀)_D^{N_{0, D}/N_{0, A}}/(f_t/f₀)_D^{N_{0, D}/N_{0, A}}-2·M₀/k_A·1/(f_t/f₀)^{N_{0, D}/N_{0, A}} (4)
Using the experimental data of (f_t/f₀)_A, (f_t/f₀)_D and the known value of N_{0, A}, N_{0, D} and M₀, k_A is calculated from the Eq. (4).
Similarly k_B, k_C and k_D are obtained.