Disentanglements

The effect of temperature on the non-catalysed reaction was difficult to disentangle, for at lower temperatures the autocatalytic reaction intervened. However, from a limited range of results, the reaction appeared to have an experimental activation energy of c. +71 kj moh. ... 

It has already been mentioned that polymer melts are non-Newtonian and are in fact under normal circumstances pseudoplastic. This appears to arise from the elastic nature of the melt which will be touched on only briefly here. In essence, under shear, polymers tend to be oriented. At low shear rates Brownian motion of the segments occurs so polymers can coil up at a faster rate than they are oriented and to some extent disentangled. At high shear rates such re-entangling rates are slower than the orientation rates and the polymer is hence apparently less viscous. 

Viscoelastic polymers essentially dominate the multi-billion dollar adhesives market, therefore an understanding of their adhesion behavior is very important. Adhesion of these materials involves quite a few chemical and physical phenomena. As with elastic materials, the chemical interactions and affinities in the interface provide the fundamental link for transmission of stress between the contacting bodies. This intrinsic resistance to detachment is usually augmented several folds by dissipation processes available to the viscoelastic media. The dissipation processes can have either a thermodynamic origin such as recoiling of the stretched polymeric chains upon detachment, or a dynamic and rate-sensitive nature as in chain pull-out, chain disentanglement and deformation-related rheological losses in the bulk of materials and in the vicinity of interface. 

CR 3nd tp are the contributions from chain recoiling and interfacial dynamics (i.e. drag forces and disentanglement), respectively, and / ve is the viscoelastic loss function which has interfacial and bulk parts. / is a characteristic length of the viscoelastic medium, t is the contact time and n is the chain architecture factor. Fig. 21 illustrates the proposed rate dependency of adhesion energy. 

Intuitively the toughness of an interface would be expected to be related to the depth of interpenetration of the chains. Wool [32] argues that the fracture energy, r, for chain disentanglement at least, is proportional to the square of the interface thickness, which, via Eqs. 36 and 37, gives ... 

How do highly interpenetrated random coil chains disentangle to cause fracture Disentanglement is considered to occur as shown in Fig. 14, where we depict the response of an entangled chain to a constant (step function) draw ratio X as follows ... 

Fig, 14. Disentanglement mechanism (A) Tightened slack between entanglements. (B) Retraction and disentanglement by Rouse relaxation. (C) Critically connected state. 

When M M, disentanglement is nearly instantaneous but approaches tro when M 8Me, which is the strain hardened (A. 4) upper bound for chain pullout without bond mpture. For welding, the relaxation times Trq refer to the minor chains of length /(/) such that the retraction time is approximated by Tro /(/). When M > 8Me, the chains cannot disentangle completely at the Rouse time and... 

The percolation parameters (p — Pc) associated with the disentanglement process are derived as follows p is the normalized entanglement density defined as... 

Me(A) increases between entanglement points due to the retraction process at constant X. A more detailed treatment of disentanglement would account for the orientation function of the entanglements and lateral contraction, as discussed elsewhere [1]. Eq. 8.4 becomes... 

The maximum molecular weight M at which disentanglement can occur is determined when strain hardening occurs at Xc 4 such that... 

Thus, fracture occurs by first straining the chains to a critical draw ratio X and storing mechanical energy G (X — 1). The chains relax by Rouse retraction and disentangle if the energy released is sufficient to relax them to the critically connected state corresponding to the percolation threshold. Since Xc (M/Mc) /, we expect the molecular weight dependence of fracture to behave approximately as... 

At high rates of strain, or when complete disentanglement cannot occur when M > M, bond rupture occurs randomly in the network and the percolation parameter p becomes dominated by chain ends such that... 

The percolation term [p — determines the number of bonds to be broken, or disentangled such that when E chains, each with L/L entanglements per chain, interdiffuse in an interface of width X, we obtain... 

The stored strain energy in the interface of volume proportional to X is consumed in disentangling the minor chains and we obtain... 

Fig. 17. A polymer-solid interface with X sticker groups on the polymer and F-receptor groups on the solid. As the chain adsorbs strongly on the solid, it tends to disentangle from the other chains in the polymer.

This surprising equality arises because an efficient appliance saves expensive electricity at the meter, at an average retail price of 8 cents/kWli whereas one kWh of new wholesale supply is worth only 2-3 cents at the power plant. Thus, even if electricity from some future new remote power plant is too cheap to meter, it still must be transmitted, distributed, and managed for 5—6 centsAWh. It is impossible to disentangle the contribution of standards and of accelerated improvement in technology, but clearly the combination has served society well. 

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