Entanglement spacing

Fetters LJ, Lohse DJ and Colby RH, "Chain Dimensions and Entanglement Spacings , In Mark JE (Ed), "Physical Properties of Polymers Handbook", AIP Press, Woodbury, NY, 2nd Ed, 2007, Chap. 25. 

The diameter, a, of the tube corresponds to the entanglement spacing, Mg. That is, a strand of polymer having molecular weight Mg spans a random walk end-to-end distance a (Fig. 3-24). Thus, = a M/Mg, and... 

Fetters, L. J., D. J. Lohse, and W. W. Graessley. 1999. Chain dimensions and entanglement spacings in dense macromolecular systems.. Polym. Sci. Part B Polym. Phys. 37 1023-1033. 

Kinetic model for deformation of polymers. 11. Effect of entanglement spacing. Macromolecules 21 2184-2189. 

Fetters LJ, Lohse DJ, Graessley WW (1999) Chain dimension and entanglement spacings in dense macromolecnlar systems. J Polym Sci, Polym Phys Ed 37 1023-1033 Fischer EW, Bakai A, Patkowski AW, Steffen W, Reinhardt L (2002) Hettaophase fluctuations in supercooled liquids and polymers. J Non-Cryst Solids 307-310 584-601 Flory PJ (1956) Statistical thcamodynamics of semi-flexible chain molecules. Proc R Soc London A234 60-73... 

J. E. Mark, ed., Physical Properties of Polymers Handbook , Chapter 24 Chain Dimensions and Entanglement Spacings, AlP Press, Woodbury, NY (1996). 

The plateau modulus Ge defines the entanglement spacing of a polymer melt, and the entanglement molar mass Me[17]... 

Consider now a polymer block (of Za monomers) which moves relative to the matrix at a velocity V which will be determined later. The semi-block cannot reptate because it is pinned at one end. In order to move, the matrix chains which traverse the microgel formed by Za monomers must disentangle. Their number is pa= Za. For the microgel to advance an entanglement spacing d = a, each of the pa chains must reptate along it s own tube, by a tube length... 

Fii>. 6. Calculated stress-strain curves obtained for linear polyethylene (M= 475,000) at four different values — indicated in graph — of the entanglement spacing factor 0 (see text). 

Fig. 4. Dependence of morphology on degree of dilution

L. J. Fetters, D. J. Lohse, R. H. Colby, Chain dimensions and entanglement spacings, in JE Mark (Ed.), Physical Properties of Polymers Handbook, AIP Press, New York, 1996, pp. 335-340. 

Reptation theory is formulated in terms of four parameters N, b, and the entanglement spacing (or, alternatively, the tube diameter) a. If a were known, and r]o could be calculated through ... 

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