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Additionally, we identify and enumerate clusters of entanglement points with high functionality as effective topological constraints on macromolecular chains.
Entanglement between the other molecules was assumed by a repulsive interaction between the chain and randomly located entanglement points.
The load was transferred to the fabric through a set of fibers linked to the entanglement points, which formed an active skeleton.
The fraction of fibers in the skeleton depended on the orientation and it was controlled by the features of the entanglement points.
The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mceff.
As concentration is increased above the critical value for network formation, the platelets are stretched into narrow ribbons connected at entanglement points.
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As the "dangling ends," which are the polymer chain segments attached to the network by only one entanglement point, do not contribute to the G value, because they cannot store elastic energy, a correction is needed in (7) [ 46]: (8) G ≅ R · T · c M e 1 − 2 M e M n, where M n is the number average molecular weight.
As G is proportional to the number of entanglements [ 36], the elastic modulus can be expressed through (5) G ≅ R · T · z, where RT is the thermal energy and z is the number of the entanglements points or cross-linking point expressed in mol/volume.
Using the "equivalent network model" [ 47], it is possible to give an estimation D N which is the average distance between the entanglements points or cross-linking points, in an idealized "equivalent network": (9) D N = 6 · M e π · c · A 3, where A is Avogadro's number.
Pang calls this "entanglement," and he points to ancient examples — such as soldiers feeling that swords were extensions of their bodies — to illustrate how core this is to the human condition.
"You would have to have two pieces of equipment in place – an entanglement generator in point A and an entanglement receiver in point B," said Perkowitz.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com