Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks

Abstract

The theory of rubber elasticity relates the elastic modulus of unfilled amorphous rubber to the concentration of elastically effective strands. A theoretical relation between this concentration and the concentrations of potential entanglements, random tetrafunctional crosslinks, and chain ends was proposed recently. In the present work, the new relation was combined with the theory of rubber elasticity and verified experimentally. Polydimethylsiloxane samples were cured by 60Co irradiation and were extensively extracted to determine gel fraction, which was used to calculate concentrations of crosslinking and scission due to irradiation. Equilibrium modulus values determined from creep tests were in excellent agreement with those calculated using the new relation if the average spacing between potential entanglements is 116 (CH3)2SiO units. Thus, in typical commercial silicone rubbers, the contribution to the modulus from trapped entanglements is greater than the direct contribution from crosslinks. The new relation allows the calculation of crosslink concentrations from modulus measurements on other unfilled rubbers once the potential entanglement spacing of the polymer is determined.

Influence of PE/PP ratio and ENB content on the degradation kinetics of γ-irradiated EPDM

“…The 6 and 2 factors account for their different mechanical efficiency (see Appendix C for additional comments). Elastically active subchains created by trapped entanglements density must also be taken into account [33,34], leading to the following equations:…”

“…The Langley [33,34] and CharlesbyePinner [35] equations are derived from a statistical description of random scission and crosslinking of polymer chains whose molecular weight distribution is assumed to be random (actually, the CharlesbyePinner equation can also be derived from the Langley approach). The elastically active chain density is deduced by considering the probability for a crosslink monomer to link two, three or four active chains to the percolating elastic network.…”

The glass transition temperature (Tg) as an index of chemical conversion for a high‐Tg amine/epoxy system: Chemical and diffusion‐controlled reaction kinetics

“…Such a consideration has been invoked in other work relating the tensile modulus to the concentration of elastically effective strands in rubber networks. 42 Therefore, the concentration of the effective crosslinking units is given by where . The model provides a good correlation for the experimental data over the entire conversion range, although a few of the data at high conversion (between 85% and 95% ) appear to lie below the calculation results.…”

Elastic modulus and equilibrium swelling of networks crosslinked by end-linking oligodimethylsiloxane at solution state

“…The contribution of trapped entanglements to elastic modulus has been disputed since the latter half of the 1970's. The central subject of the dispute has been that trapped entanglements contribute to elastic modulus together with chemical crosslinks [1][2][3][4][5][6] or not. [7][8][9] In order to settle this problem, the elastic moduli of ''model polymer networks'' ͑which are prepared in bulk state by end-linking prepolymer having a definite molecular weight͒ have been measured as a function of molecular weight of prepolymer (M p ).…”