Entanglement distance polymers

In the packing model [50,62,68] the entanglement distance is interpreted by the gradual build-up of geometrical restrictions due to the existence of other chains in the environment or, more precisely, the entanglement distance is determined by a volume which must contain a defined number of different chains. This approach is based on the observation that, for many polymer chains, the product of the density of the chain sections between entanglements is... 

Fig. 29. Double logarithmic representation of the entanglement distance in polyethylene at 509 K as a function of the polymer volume fraction >. (Reprinted with permission from [60]. Copyright 1993 American Chemical Society, Washington)...

Richter D, Farago B, Fetters LJ, Fiuang JS, Ewen B, Lartique C (1990) Direct microscopic observation of the entanglement distance in a polymer melt. Phys Rev Lett 64 1389— 1392... 

Both the questions of the transition from Rouse to reptation dynamics and of what fixes the average distance between entanglements in polymer liquids has been the subject of a number of recent theoretical and experimental investigations. 

Another quantity of interest in semidilute solutions is called the blob. It contains a number of mers on the same chain defined by the mesh volume inside of which excluded volume effects are operative. Some texts define the blob as the number of mers between adjacent entanglements, distance s apart. These blobs are large enough to be self-similar to the whole polymer chain coiling characteristics they are coils within a coU. The concept of the blob has been important in theoretical calculations. With increasing concentration, the blobs become smaller, becoming equal to that of an individual mer in polymer melts (no sovent). 

This network model was developed for PS with its relatively large entanglement distance d of about 10 nm and average mesh diameter D (Z) = d Vi = 1.4d) of about 14 nm. However, it can also be used for other amorphous polymers with smaller entanglement molecular weights and distances. These density fluctuations in a domain-like form are the weakest supramolecular structures in amorphous polymers. Therefore, the typical amorphous polymers, often used as models of an amorphous material, are also not really structureless. In the literature, there are some other results relating to the structures of amorphous polymers, ranging... 

Under quiescent conditions, polymer solutions are divided into four categories depending on the average distance separating the centers of mass of the molecular coils the dilute, the semi-dilute (or semi-concentrated), the concentrated and the entangled state. 

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

Fig. 1.2 Richness of dynamic modulus in a bulk polymer and its molecular origin. The associated length scales vary from the typical bond length ( A) at low temperatures to interchain distances ( 10 A) around the glass transition. In the plateau regime of the modulus typical scales involve distances between entanglements of the order of 50-100 A. In the flow regime the relevant length scale is determined by the proper chain dimensions...

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