Coil-to-stretch transition

If e is now decreased, with the chain in the extended state, the dumbbell nevertheless stays in the stretched state where the potential is the lowest. The transition back to the coiled state occurs only when there is a single minimum on the potential energy curve, i.e. at et = 0.15. Since the critical strain-rate for the stretch-to-coil transition (esc) is much below the corresponding value for the coil-to-stretch transition (eca), the chain stretching phenomenon shows hysteresis (Fig. 11). 

A plausible assumption would be to suppose that the molecular coil starts to deform only if the fluid strain rate (s) is higher than the critical strain rate for the coil-to-stretch transition (ecs). From the strain rate distribution function (Fig. 59), it is possible to calculate the maximum strain (kmax) accumulated by the polymer coil in case of an affine deformation with the fluid element (efl = vsc/vcs v0/vcs). The values obtained at the onset of degradation at v0 35 m - s-1, actually go in a direction opposite to expectation. With the abrupt contraction configuration, kmax decreases from 19 with r0 = 0.0175 cm to 8.7 with r0 = 0.050 cm. Values of kmax are even lower with the conical nozzles (r0 = 0.025 cm), varying from 3.3 with the 14° inlet to a mere 1.6 with the 5° inlet. In any case, the values obtained are lower than the maximum stretch ratio for the 106 PS which is 40. It is then physically impossible for the chains to become fully stretched in this type of flow. 

A discontinuous coil to stretch transition is evident at sc = 0.000725. The transition point sc was found by using two different initial conformations as described above. For values lower than ec> the random chain will eventually coil, form a folded chain crystalline structure and stay in that conformation until the end of the run for relatively long run times. On the other hand, a prestretched chain would fluctuate and eventually form a crystallized folded chain that is stable. Similarly, for flow rates higher than sCy a pre-stretched chain will never coil and a random chain will eventually stretch. 

Dilute solutions of flexible chains in extensional flow are predicted to undergo a coil-to-stretch transition when the strength of the flow reaches a critical value relative to the inverse of the longest relaxation time, x, of the chains. This criteria is met when [147]... 

Fig. 1 Coil-to-stretch transition (CST) of a polymer chain. The flow direction is vertical. The red arrows highlight the end-to-end distance R of the chain...

First, we measured the flow rate dependent relative retention [(Co — C)/Co] of hyperbranched polystyrene fractions by gradually increasing the flow rate. Figure 5.9 shows that (Co — C)/Co decreases as the flow rate increases but not as sharp as the first-order coil-to-stretch transition of linear chains observed before [38, 43]. Presumably, this is because even for a given overall molar... 

Fig. 11. Hysteresis in the coil-to-stretch (CS) and stretch-to-coil (SC) transitions. For reversible situations, the transition from (S) to (C) should take place at a particular value of the strain rate (e ) through an unstable state (P). In practice, hysteresis is expected and should involve the cycle shown by arrows...

The maximally attainable helical content is strongly dependent on the amount of precursor units present in the chain (Figure 2). Both data from polarimetry as well as from DSC indicate that the temperature of the coil-to-helix transition is independent of the amount of precursor units present (Figures 2 and 4). It is therefore concluded that the presence of v-units does not lower the stability of the helical stretches. On integration of the DSC signal from the temperature of the... 

The results led us to postulate that this behaviour is due to the presence of a stagnation point. In fact, the flow at the upstream of this stagnation point is strongly elongational and therefore able to give rise to a strong deformation of macromolecules corresponding to a coil t stretch transition. 

The electrochemical method used, was proved to be very sensitive and it has been shown, for the first time, that fluctuations are associated with the transition. The onset of these fluctuations has been explained in terms of an hydrodynamic instability induced by a viscosity stratification which is generated by the coil t stretch transition. 

As early as 1932 Trommsdorf [141] and Staudinger [142] observed the viscosity of PMA in pure water to increase dramatically with decreasing polyion concentration. The same observations were made later by Kern [143]. This is in contrast to the viscosity behaviour usually found for neutral polymers. Later, Fuoss and Strauss developed their famous empirical extrapolation and explained the polyelectrolyte effect by a coil-to-rod transition because, upon dilution, the ionic strength decreases, eventually leading to a fully stretched polyion as anticipated at the time. 

As will be discussed in the next section, the shift of tf with increasing eN (Fig. 7.20) can be interpreted as resulting from an onset of chain stretching. While experimentally it was suggested that the transition from Gaussian coils to stretched chains that occurs at a temperature T above Tc is rather sharp, the more complete simulation data on this point show that this stretching of the chains sets in very gradually. 

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

At a higher temperature T = 11.0, for flow rates near the transition rate c, the free-energy barrier between the coiled and stretched conformation is much lower than that for T = 9.0. The chain can therefore explore the phase space and jump back and forth from the coiled to the stretched state. Similar behavior has already been observed in [59] and [60]. Figure 27 illustrates this feature. 

K. Almdal, J. H. Rosedale, F. S. Bates, G. D. Wignall, and G. H. Fredrickson, Gaussian-to stretch-coil transition in block copolymer melts, Phys. Rev. Lett., 65, 1112 (1990). 

It is important to point out that this coil-stretch transition mechanism for interfacial slip does not require the adsorbed chains to stay permanently anchored to the wall. The polymer melt adsorption only needs to be strong enough to keep adsorbed chains tethered onto the surface for as long as it takes for them to undergo the stress-induced coil-stretch transition. Approximately, this residence... 

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