Number of entanglement strands per

The plateau modulus is given by the usual formula for entangled polymers, Gq vksT, where v is the number of entanglement strands per unit volume of melt that is,... 

The average contour length (L) of the primitive path (the centre of the confining tube, see Fig. 7.10) is the product of the entanglement strand length a and the average number of entanglement strands per chain N/N. ... 

Lin, Y. -H. Number of entanglement strands per cubed tube diameter, a fundamental aspect of topological universahty in polymer viscoelasticity. Macromolecules, 1985,... 

Number of Entanglement Strands per Cubed Entanglement Distance, rit... 

Corresponding to Eq. (13.4), the number of entanglement strands per cubed entanglement distance for the blend solution is now defined by... 

Lin Y. H. (1987). Number of Entanglement Strands per Gubed Tube Diameter, a Fundamental Aspect of Topological Universality in Polymer Viscoelasticity. Macromolecules, 20(12), 3080-3083. 

With the number of entanglement strands ne/volume, the desired number of binary contacts per entanglement strand becomes... 

Fig. 40a. Craze fibril stability (e — e ) versus n, the mean number of effectively entangled strands per fibril for monodisperse PS (circles) PS molecular weight blends (squares) monodisperse PMMA (diamonds) and monodisperse PotMS (stars) The solid lines are the predictions of the model using the parameters given in the text, b Craze fibril stability (e — e ) vereus 1 / where is the mean force per effectively entangled strand in the fibrils. Same symbols and lines as in a...

A determination of how Gat depends on the chemical structure of a polymer requires a definition of an entanglement. Various ideas have been proposed a fixed number of binary contacts per entanglement (Brochard and De Gennes, 1977) or per entanglement volume (Colby et al., 1992) a fixed number of strands per entanglement volume (Ronca, 1983 Lin, 1987 KavassaUs and... 

As in the previous chapters, it has been assumed that the number of (Kuhn) segments per entanglement strand, Ng, is sufficiently large so that the mean square end-to-end distance of an entanglement strand can be expressed as... 

The plateau modulus in this regime is G VefeeT, where Ve is the number density of entanglement strands. The volume per entanglement strand is =fa. The scaling model... 

Tnteractions are not important. The dynamics on these intermediate scales (for r < t< Te) are described by the Rouse model with stress relaxation modulus similar to the Rouse result for unentangled solutions [Eq. (8.90) with the long time limit the Rouse time of an entanglement strand Tg]. At Te, the stress relaxation modulus has decayed to the plateau modulus Gg[kT per entanglement strand, Eq. [(9.37), see Fig. 9.9)]. The ratio of osmotic pressure and plateau modulus at any concentration in semidilute solution -in athermal solvents is proportional to the number of Kuhn monomers in ... 

Consider a molecule made out of two /-arm stars with Kuhn segments per arm with junction points connected by a central linear strand of Abb Kuhn monomers. This molecule is called a pom-pom polymer. If/= 1, this molecule is linear, while the H-polymer corresponds to /=2. Estimate the /-dependence of relaxation time and diffusion coefficient of a melt of monodisperse pom-pom polymers for /> 1. Consider only single-chain modes and assume that the coordination number of an entanglement network is z. 

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