Mechanism
Entangled polymers are characterized with effective internal scale, commonly known as the length of macromolecule between adjacent entanglements .
Entanglements with other polymer chains restrict polymer chain motion to a thin virtual tube passing through the restrictions. Without breaking polymer chains to allow the restricted chain to pass through it, the chain must be pulled or flow through the restrictions. The mechanism for movement of the chain throught these restrictions is called reptation.
In the blob model, the polymer chain is made up of Kuhn lengths of individual length . The chain is assumed to form blobs between each entanglement, containing Kuhn length segments in each. The mathematics of random walks can show that the average end-to-end distance of a section of a polymer chain, made up of Kuhn lengths is . Therefore if there are total Kuhn lengths, and blobs on a particular chain:
The total end-to-end length of the restricted chain is then:
This is the average length a polymer molecule must diffuse to escape from its particular tube, and so the characteristic time for this to happen can be calculated using diffusive equations. A classical derivation gives the reptation time :
where is cofficient of friction on a particular polymer chain, is Boltzmann's constant, and is the absolute temperature.
The linear macromolecules reptate if the length of macromolecule is bigger than ten times . There is no reptation motion for polymers with, so that the point is a point of dynamic phase transition.
Due to the reptation motion the coefficient of self-diffusion and conformational relaxation times of macromolecules depend on the length of macromolecule as and, correspondingly. The conditions of existence of reptation in the thermal motion of macromolecules of complex architecture (macromolecules in the form of branch, star, comb and others) have not been established yet.
The dynamics of shorter chains or of long chains at short times is usually described by the Rouse model.
Read more about this topic: Reptation
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