The Doi— Edwards equation predicts that the ratio 2 is —2/7 = —0.29 at low shear rates. This changes to 4 2/ l i = —1/7 = —0.14 when the independent alignment approximation is dropped (Osaki et al. 1981). With or without the independent alignment approximation, the ratio —is predicted to decrease towards zero as the shear rate increases. The prediction of fof entangled solutions contrasts with that predicted [Pg.164]

Ruan K, Briggman KB, Tolman JR (2008) De novo determination of intemuclear vector orientations from residual dipolar couplings measured in three independent alignment media. J Biomol NMR 41(2) 61-76 [Pg.65]

Bulk material properties can be determined quite simply using this model. For example, consider the calculation of the second-moment tensor, Q = (u u ), which is required for the stress and refractive index tensors. Using the independent alignment approximation, we have [Pg.131]

Retraction moves a strand from one part of the tube to another hence the strand s orientation is determined not by the orientation of the part of the tube it originally occupied, but by the orientation of the part of the tube into which it moves. To simplify the problem, however, Doi and Edwards invoked the independent alignment approximation, which assumes that after retraction each strand is oriented independently of the others, and the change in orientation produced by retraction is neglected. [Pg.159]

Curtiss and Bird introduce reptation in a maimer which does not involve the tube concept, at least not in an explicit way. Their model leads to a constitutive equation in which the stress is the sum of two contributions. On contribution is exactly 1/3 the expression obtained by Doi and Edwards when those workers invoke the independent alignment approximation, i.e., that contribution is a special case of the BKZ relative strain equation. The othCT contribution depends on strain rate and is proportional to a link tension coefficent c (0 < e < 1) which diaracterizes the forces along the chain arising from the continued displacements of chain relative to surroundings. [Pg.108]

Fig. 18.13 Comparison of the simulation values ( ) of —N2 t,X)/Ni(t,X) in the slowmode region obtained from the present study and the experimental valnes (o) in the terminal region of the entangled system studied by Osaki et al. with the curve (solid line) numerically calculated from the Doi—Edwards expression (Elq. (12.17)) with the independent-alignment approximation. |

Fig. 7.16. h(Y) determined from the procedure explained in Fig. 7.15. Filled circles represent polystyrene of molecular weight 8.42 xlO and the unfilled circles of 4.48 x 10 . Directions of pips indicate concentrations which range from 0.02 g cm to 0.08 g cm. The solid curve rqnesents the theoretical value (eqn (7.131)), and the dashed curve the result of the independent alignment approximation (eqn 7.187). Reproduced from ref. 69. |

© 2019 chempedia.info