Chain retraction

Fig. 16. Chain retraction in a tube under non-linear strain...

The process of chain retraction can be applied to more complex topologies of entangled polymers under the same assumptions discussed for linear polymers... 

A simple RIS model of polymers in elongational flows is developed and used to analyze the coil stretching and chain retraction as a function of polymer and flow parameters. The results are in agreement with available experimental data on dilute polymer solutions in strong elongation flows. 

These results, as compared to a previous study [29], illustrate a better agreement between theory and experiments. This can be attributed to a better approximation of the mode distribution involved in the chain fluctuation process and to which the end of the chains are quite sensitive. These data also prove that under our experimental conditions, the relaxation of the chain is dominated by the chain retraction and chain-length fluctuation process. The... 

As the water uptake proceeds, the increased sidechain-counterion dissociation allows for more complete ionic hydration. The deformation of the polymer chain network upon further incorporation of water molecules also proceeds by a shift in the distribution of rotational isomers to higher energy conformations and changes in other intramolecular, as well as intermolecular interactions. Consequently, the increased overall energy state, for a given membrane water content of n moles, per equivalent of resin, is manifested by polymer chain retractive forces that resist expansion of the network. Accordingly, the configurational entropy decreases as less conformations become available within the matrix. Eventually, an equilibrium water content, nQ, is... 

Shanbhag, S., and Larson, R. G., 2005. Chain retraction potential in a fixed entanglement network, Phys. Rev. Lett., 94(7) 076001. 

The basic idea, proposed by de Gennes [23], is that relaxation mechanism of linear pendant chains is governed by the reptation or snake-like motion of the chains retracting along their primitive path from the free end to the fixed one. This model proposed that the relaxation time of pendant chains should increase exponentially with the number of entanglements in which it is involved. Pendant chains must then contribute to viscoelastic properties for frequencies greater than the inverse of reptation times. Tsenoglou [26], Curro and Pincus [27], Pearson and Helfand [24] and Curro et al. [25] developed models for the relaxation of pendant chains in random cross-linked networks. 

Fig. 44. Schematic of the stress relaxation process after a large step in deformation, (a) Equilibrium conformation of the tube prior to deformation, (b) Immediately after deformation, the primitive chain has been affinely deformed, (c) After the time Xr, the primitive chain retracts along the tube and recovers its equilibrium contour length (t=XR). (d) After the time Xd the primitive chain leaves the deformed tube by reptation (t=Xa). After Doi and Edwards (56), with permission.

K. Osaki, H. Watanabe, and T. Inoue, Damping Function of the Shear Relaxation Modulus and the Chain Retraction Process of Entangled Polymers Macromolecules 29, 3611-3614(1996). 

Rubber is elastic, and gooey liquids such as raw eggs are viscoelastic, because polymer molecules have many conformations of nearly equal energy. Stretching the polymer chains lowers their conformational entropy. The chain retract to regain entropy. The entropy is also lowered when polymers become compact, as w hen proteins fold or when DNA becomes encapsulated within virus heads. The simplest molecular description of polymer elasticity is the random-flight model. 

Osaki K, Watanabe H, Inoue T (1996) Damping function of the shear relaxation modulus and the chain retraction process of entangled polymers. Macromolecules 26 3611-3614... 

Chain retraction potential in a fixed entanglement network. Phys. Rev. Lett.. 

Typical plots of the specific viscosity, against the logarithm of salt (NaCl) concentration Cg, are given in Fig. 4.1. As expected, for both the precursor poly(sodium acrylate) and the modified sample 3-C18 (containing 3 mol% of octadecylacrylamide groups), the viscosity decreases monotonically as the NaCl concentration increases. However, the modified polymer exhibits a more pronounced viscosity decrease when the salt concentration is higher than about 0.3%. In the case of the precursor polymer the decrease in viscosity is due only to the screening of the electrostatic interactions. The modified polymer seems to follow the same mechanism at low salt concentrations but apparently at Cg > 0.3% another mechanism contributes to some additional chain retraction. 

Figure 10.1 Sketch illustrating chain retraction. We see affine deformation of the matrix of constraints (represented by dots) as well as the tube, followed by retraction of the chain within the tute. Affine deformation implies that the microscopic deformation equals the macroscopic strain. After retraction, the chain deformation is non-affine, and the primitive path equals that at equilibrium (drawing from [228]).

Equations 11.23 through 11.26 are the counterparts to Eqs. 11.14 through 11.17 of the MED theory. In Eq. 11.23, the CCR term is just Ir S, similar to the CCR term K S - XlA) in the MED theory, but without the transient chain retraction rate A/ /I. (In Eq. 11.23, an absolute value must be taken of the CCR term at S to keep its value positive, while in the MED theory, this term is kept positive through the stretch equation 11.16.) The expression Eq. 11.23 for the orientational relaxation time contains not only the reptation time and the rate of convective constraint release k S, but also the stretch time t. This guarantees that even for velocity gradients greater than 1 /Tj, the rate of orientational relaxation remains bounded by 1 /Tj. This effectively switches off the CCR effect for fast flows, and so functions in much the same way as the switch function/(A) in the MED theory. Hence, no explicit switch function is present in Eq. 11.23. 

Thus nonlinear constitutive equations that describe reptation, time-dependerrt chairr retractiorr, and constraint release by reptation and chain retraction, are in promisingly good agreemerrt with nonlinear data in shear flows of monodisperse or bidisperse entangled polymer solutiorrs. To be of use in practical polymer processing applications, however, such equations must be accurate for melts of polydisperse polymers. In steady shear flows of polymer melts, the steady-state viscosity as a function of shear rate T] y) is frequently found to be numerically roughly equal to the dynamic shear viscosity as a function of frequency tf (o) = [ tj io)) +, ... 

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