Slip link

Figure 2 Schematic drawing of a slip link, with its possible motions along the network chains specified by the distances a, and its locking into position as a cross-link.

The elastic free energy of the constrained-junction model, similar to that of the slip-link model, is the sum of the phantom network free energy and that due to the constraints. Both the slip-link and the constrained-junction model free energies reduce to that of the phantom network model when the effect of entanglements diminishes to zero. One important difference between the two models, however, is that the constrained-junction model free energy equates to that of the affine network model in the limit of infinitely strong constraints, whereas the slip-link model free energy may exceed that for an affine deformation, as may be observed from Equation (41). 

An intermediate situation is obtained if the central crosslink is replaced by a slipping link such that the two chains are constrained to be in contact at one... 

Fig. 7.2 Mooney-Rivlin plot for the Slip-Link model...

Figure 3. Slip-link joining two network chains. The slip link is assumed to slide a distance a along the chains [3],...

M. H. Wagner and J. Schaeffer, Constitutive Equations from Gaussian Slip-link Network Theories in Polymer Melt Rheology, Rheol. Acta, 31, 22-31 (1992). 

The first relaxation process (designated A hereafter) corresponds to a Rouse-like relaxation of chain segments between entanglement points. It is assumed that the entanglement points remain fixed during the time-scale of this relaxation and that no diffusion of monomers through the slip-links is allowed in such short times. The associated relaxation time,, is related to a monomeric friction coefficient, to thie number of monomers between... 

Figure 8 Relaxation of a polymeric chain after a step-strain deformation[6] process A (8c) reequilibration of chain segments process B (8d) reequilibration across slip links process C (8e) reptation.

The first relaxation process (called the A relaxation process Fig. 8c) which occurs at the shortest times will be a local reequilibration of monomers without slippage through the slip-links. In other words, it is basically a Rouse relaxation process between entanglement points which are assumed to be fixed in that time scale. The characteristic relaxation time of this process is rather short and is independent of the overall chain length (see below). 

The second relaxation process (B process Fig. 8d) is a reequilibration of segments along the overall chain, i.e., across slip-links. It is basically a retraction of the chain to recover its natmal curvilinear monomer density, which may be depicted as a Rouse relaxation process along the entire chain. 

Viovy [8] describes that re-equilibration process as an exchange of monomers between neighbouring segments he calls that process "reequilibration across slip-links", and tlie corresponding relaxation hmction may be written as ... 

M.H.Wagner, J.Schaeffer, Constitutive equations from Gaussian slip-link network theories in polymer melt rheology, Rheol. Acta 31 (1992), 22-31. 

Higgs, P. G. and Ball, R. C. 1990. A reel-chain model for the elasticity of biopolymer gels, and its relationship to slip-link treatments of entanglements, in Physical Networks. Polymers and Gels, eds. W, Burchard and S. B. Ross-Murphy, Chapter 15, Elsevier Applied Science Publishers, Barking, England. 

As discussed below in this chapter, the Doi-Edwards theory models entanglements as slip-links. Having taken the effects of chain slippage through the links into account, the theory gives ... 

Fig. 8.1 Equivalence of (a) the tube picture and (b) the slip-link picture with the hypothetical tensile force Feq = ikT/a pulling at both chain ends in describing the constraint effect of entanglement on the movement of a polymer chain.

Fig. 8.2 In the slip-link model, a hypothetical tensile force Feq = ikTja pulling at both chain ends is necessary to keep the polymer chain constrained by the slip-links otherwise, the polymer chain will soon shrink along the primitive path and leak out from the space between the slip-links or, so to speak, leak out of the tube.

Assume that, at time t <0, the polymeric liquid system is in the equilibrium state, and a particular chain constrained by the slip-links in the system has a configuration as shown in Fig. 8.3(a). At t = 0, a step deformation E is applied to the system, and the configuration of the chain together with the slip-links is immediately changed to that shown in Fig. 8.3(b). At this stage, the stress tensor is given by ... 

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