Entangled light

Figure 4.53 Schematic illustration of the reptation process in polymer melts, showing chain entanglements (light arrows), the wriggling motion of the polymer chain (darker arrows), and the primitive path of the polymer chain (dark Une). Reprinted, by permission, from G. Strobl, The Physics of Polymers, 2nd ed., p. 283. Copyright 1997 by Springer-Verlag.

The E-modulus appeared to be inversely proportional to the distance between crosslinks, so, approximately, proportional to the number of cross-links. If no permanent cross-links are present, i.e. in the unvulcanized condition, then E is governed by the number of physical entanglements. Light vulcanization does not contribute significantly to total number of cross-links therefore, in lightly crosslinked vulcanizates, such as technical rubbers, the E modulus is hardly dependent on the degree of vulcanization (Qu. 5.4 en 5.5). 

M. Kiffner,M. S. Zubairy,J. Evers, C. H. Keitel. Two-mode single-atom laser as a source of entangled light. Physical Revew A 2007 Jul 2 75(3) 033816(8). 

Figure 9.1. Schemalic illuslralion of dependence of Ihe modulus of a polymer on a variety of factors. A is an amorphous polymer of moderate molecular weight whereas B is of such a high molecular weight that entanglements inhibit flow. Similar effects are shown in C and D, where the polymer is respectively lightly and highly cross-linked. In E and F the polymer is capable of crystallisation, F being more highly crystalline than E...

If the ideas of Marrucci [69] are correct and the non-monotonic predictions of the simple Doi-Edwards theory need to be modified in the case of polymer melts (for a recent development see [78]), then an explanation will be required for the apparent difference at high shear rates between melts and wormlike micelle solutions. There is also evidence that ordinary entangled polymer solutions do exhibit non-monotonic shear-stress behaviour [79]. As in the field of linear deformations, it may be that a study of the apparently more complex branched polymers in strong flows may shed light on their deceptively simple linear cous-... 

The above results are certainly unexpected in light of an earlier report on adhesion of polyimide films [47]. Here it was shown that adhesion between two polyimide films could only be achieved when polyimide chains from the one surface extended approximately 300 A into the other surface. Because of the extended nature of the polyimide chains the potential for significant entanglements near the respective interfaces is low, thus requiring much deeper penetration by the PI to provide the necessary frictional forces for good adhesion. In the... 

Worsfold found that the degree of association as measured from viscosity was less than that indicated by the light scattering and spectroscopic results. It was therefore concluded that the association dissociation rates were comparable to the chain entanglement lifetime. As a consequence, Worsfold concluded that viscosity measurements involving concentrated solutions of poly(dienyl)lithium in the entanglement regime could not detect the presence of, for example, star-shaped tetramers if the equilibrium... 

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