# Self-consisting modeling of entangled network strands and dangling ends

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- The Society of Rheology
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## Abstract

Text of Abstract We seek knowledge about the effect of dangling ends and soluble structures of stoichiometrically imbalanced networks. To interpretate our recent experimental results we seek a molecular model that can predict LVE data. The discrete slip-link model (DSM) has proven to be a robust tool for LVE and non-linear rheology predictions for linear chains, and it is thus used to analyze the experimental results. We divide the LVE predictions into three domains; 1) the low frequency region, where G' is a plateau, G0, 2) the intermediate frequency region, where G' and G'' are parallel and 3) the high frequency region, where G' levels off to an entanglement plateau, GN0, close to that of the linear polymer. The latter region is seldom obtained in experiments, while it is obtained in simulations since these start at zero time. Initially we consider a stoichiometrically balanced network, we call this an ideal entangled network (IEN). We simulate monodisperse polypropylene oxide with an average number of entanglements of ~3.8. Such lightly entangled networks show a G0 that is about 24% lower than GN0. This decrease is a result of monomer fluctuations between entanglements. Additionally we observe that G' is dominating at all frequencies compared to G''. Experimental observations of stoichiometrically imbalanced networks shows that G'' and G' are of the same order of magnitude at intermediate frequencies, hence the DSM suggests that energy dissipation is largely a result of dangling ends and soluble structures. Energy dissipation is increased by adding a fraction of dangling ends, wDE, to the ensemble. We find that when wDE=0.6, G0 is about 75% lower than GN0, this suggests that the fraction of network strands, wNS=1-wDE, largely influences the plateau value at low frequencies. Soluble strands can also be added to the theory which is expected to increase energy dissipation further.

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