Crosslinking,filler, or transition constraint of polymer networks. I |
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Authors: | A F Blanchard |
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Abstract: | The basic theory of modulus/swelling is developed to allow for limited extensibility, filler reinforcement or transition effects, and steric hindrance of aligned segments by extended chains or filler particles. Filler forms an effective hard fraction Ch per cubic centimeter of compound with vc a new (compound) index of swelling. For 1/Mc + σ fix points having ratio φ to gum values 1/F0(vr) and with F(vc) replacing the Flory function F(vr): where σ denotes entanglement. Linkage reinforcement φ does not vary with sulfur crosslinking of SBR. Vacuoles invalidate φ from mass-increment F0(vr)/F(vr) for inert fillers. Then, or for Graphon, with negligible φ ≈ 1: The effective Ch includes rubber stretched hard on Graphon by swelling or trapped inside hard aggregates. Only the right-hand equation fits normal blacks. In theory, Ch can always be obtained from swollen moduli G by linear slopes (1 + 1.4Ch) relating F(vc) and (1 ? C)ρRT/G. For filler fractions C ≥ 0 cm?3 and low strains α = 1.5?2.0 below prestretch the modulus G is given a new basic definition: Here C2* ≈ 0.7 corresponds to Mooney-Rivlin C2 and the effective crosslinking 1/Mc] = (ρRT)?1G is equal to (1 ? C)(1/Mc + σ) for unswollen prestretched rubber (vr = 1). For higher strains a hypothesis of strain hardening is proposed. This is distinct and opposite in character to the initial prestretch softening (Mullins effect). Nonlinear effects of crosslinks are expressed by a fractional stress-upturn Ω (1/Mc + σ), effective mesh wieght (1/Mc + σ)?1 ? Ω, and hard fraction Ω(1/Mc + σ). For μh characterizing strain hardening up to the prestretch (αh ? 1) their contribution is: The sixth-power refinement has J = j(αb ? 1)1/2 with j ≈ 0.4. The hard phase is augmented by filler and grows with increasing strain up to the prestretch. |
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