Multiaxial deformations of end-linked poly(dimethylsiloxane) networks. 4. Further assessment of the slip-link model for chain-entanglement effect on rubber elasticity

Abstract

The Edwards–Vilgis slip-link model for the chain-entanglement effect on rubber elasticity is critically assessed on the basis of quasiequilibrium biaxial stress—strain data of end-linked polydimethylsiloxane (PDMS) networks with different entanglement densities. The PDMS networks with different entanglement densities were prepared by end-linking end-reactive long precursor PDMS in solutions with different solvent contents. The slip-link model, in which trapped entanglement is modeled by fictitious mobile slip-link attaching two entangled chains, satisfactorily describes the biaxial data over the entire range of deformation for all the networks examined. The model-specific parameters, i.e., slippage of slip-link (η) and inextensibility of network (α), were employed as adjustable parameters in data-fitting. The fitted values of η and α vary reasonably with the degree of dilution at network preparation, i.e., entanglement density. With an increase in dilution, i.e., decrease in entanglement density, η increases, whereas α decreases. In addition, the fitted values of η and α are in good agreement with the estimates from another molecular approach independent of mechanical testings: η=Me/Mc, where Me and Mc are the molecular masses between neighboring entanglements and between adjacent cross-links, respectively; α=nj−1/2, where nj is the number of Kuhn segments between adjacent elastically effective junctions including cross-links and trapped entanglements. The satisfactory data-fit with the model parameters of physically reasonable magnitudes supports the validity of the slip-link model for entanglement effects on rubber elasticity.