Size and Form of the Macromolecular Coil

A macromolecular coil at equilibrium has a spherical form (Section 1.4). Under deformation of the system, the macromolecular coil change its form that is characterised in this case by the tensor of gyration 

In normal co-ordinates, to which we transform in accordance with the rule defined by (1.13), the expression for the tensor of gyration acquires the form 

This relation is valid both for the macromolecular coil in a viscous liquid and for the macromolecular coil in an entangled system. 

At constant velocity gradient Xik, the moments (pfpk) are given by relations (4.46) for the diffusive mechanism of relaxation, and by similar formula (there is a difference in definition of the relaxation times only) for the rep-tation mechanism, so that we can evaluate the expression for the tensor of gyration of the macromolecular coil, taking into account alternative mechanisms of relaxation 

The function of density distribution p(r) can also be introduced in the non-equilibrium state it must now satisfy the following conditions 

---

To characterise the size and form of the macromolecular coil, one can introduce a function of density of the number of particles of the chain... 

The mean size and form of the macromolecular coil is characterised by the set of the tensors (pf / , a = 1,2,..., N. To describe relaxation of macromolecular coil, it is convenient to use the non-dimensional tensor variables... 

---