Dynamics_Polymer_Networks_Phys_Scripta_Edwards_1991 -...

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Physica Scripta. Vol. T35, 11-16, 1991. Dynamics of Polymer Networks S. F. Edwards Cavendish Laboratory, Cambridge CB3 OHE, U.K. Received April 9, 1990: accepted January 30, 1991 Abstract the polymer 2 by V = 7cYa2. But A = CVSO that a - c-”~, Simple models of the behaviour of polymers in networks are shown to be translatable into equations of motion and hence to equations of viscoelasticity. These simplest models have notable success, but there are disturbing features in scattering experiments and in ‘second order’ theoretical analysis which are discussed but not resolved. 1. Introduction Polymeric networks are a major subdivision of condensed matter and offer a challenge to physicists of a different nature to other branches of condensed matter physics in that the problems are primarily topological i.e., concern the ways molecules are configured relative to one another. This paper is mainly concerned with melts i.e., pure polymer above the glass temperature, so that our material is in high thermal agitation and therefore can flow as a viscoelastic liquid, or, if permanently cross linked, is a rubbery material, but occasion- ally reference will be made to concentrated solutions i.e., melts with a swelling solvent added. A central fact is that it is possible to normalize the behav- iour of most polymer melts so that transport properties all lie where c is the arc concentration [2, 31. (In a solution the arc concentration is clearly related to the mass concentration but even in a melt, different polymers have quite different c; a bulky polymer like polystyrene having a c much smaller than polyethylene.) So our picture is now of a quickly changing local pattern in Fig. 1 leading to a slowly changing pattern of Fig. 2. Indeed Fig. 2 can only change by the polymer diffusing to form a new tube by reptation in a melt and not at all n a cross linked system. However, a deformation of the bulk material will deform the primitive path, in the simplest model affinely, so one can work out what happens again by simple pictures which are given below in Section 4. The picture offered above has a > I, but if one uses liquid crystal polymers hinged together as is now possible, one can have a situation where I B a, and materials can be thus made whose viscosity is infinite but which have no cross linkage at all. There is no time in this paper to consider these further, but there is no doubt of their future importance. on master curves. Similarly most rubbers show the same stress strain behaviour. It appears that the chemical nature of 2. Statistical mechanics of networks __ the polymer gives rise to an effective friction in the motion of the polymer relative to its surroundings and to a Kuhn length which relates the size of the polymer to its molecular weight and another Kuhn like length which characterizes the topological specification of the polymer in the melt; but that is all [l]. This means that one should be able to explain all the properties of melts and networks by simple diagrams in
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Dynamics_Polymer_Networks_Phys_Scripta_Edwards_1991 -...

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