Contour length relaxation

Contour Length Relaxation. Doi and Edwards have proposed an additional, faster relaxation mechanism for which they use the term contour length relaxation (5). As shown in Figure 3, contour length relaxation is a process by which a deformed linear (or star shaped) chain should retract towards the center of mass of the chain. Since the overall contour length increases upon deformation, the proposal by Doi and Edwards is that the deformed chain would want to resume the same chain density along the overall contour of the chain as that... 

Figure 3. Contour length relaxation after a large step strain.

This was introduced as a simple method to account for constraint release, and in its original form it does not accoimt for contour length relaxation, so that it predicts that the zero-shear... 

The applied strain is affine and the whole of the tube is deformed along with the polymer. As the strain is infinitesimally small the contour length is unaltered. At very short times / after the strain is applied, t < re tr the stress is relaxed as a Rouse chain. At short times we can make an approximation and replace our sum by an integral ... 

The viscosity relates to the longest relaxation time in a system. If we consider Rouse diffusion along the tube with a Rouse diffusion coefficient DJ l/ NQ) then an initial tube configuration is completely forgotten when the mean-square displacement along the tube fulfils (r (t))tube=(contour length ly. Thus, for the longest relaxation time, we obtain ... 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

It has been shown by Doi [11] that on the time scale of Tg contour length fluctuations may induce a rapid relaxation of chain ends, especially for moderately long chains. Indeed, wiggling motions involve forward and backward motions of the chain ends. Thus, chain length fluctuations in oriented materials lead to the creation of isotropic parts of tubes at each end. Their fractional length is roughly equal to 1.3(N e) > where N is the number of monomers per chain. An elaborate expression for the relaxation due to this mechanism, based on the Pearson-Helfand picture for star pol5uners [12], has been proposed by Viovy [13]. 

Assuming that the tightly bound counterions move in a square well potential [69] with a length of L (its upper value is the polyion contour length), Ookubo et al. [25] calculated from the critical frequency of LF relaxation the diffusion constant of these ions Dl... 

A second effect of platination was noted (18) on the electrophoretic mobility of relaxed circular DNA. The mobility of this form increased with increasing platinum binding, as opposed to the initial decrease and subsequent increase in mobility of supercoiled DNA. This behavior was attributed to a shortening of the DNA due to platiniim induced crosslinks. Further evidence was obtained from electron micrographs of the platinated DNA samples (18,24)f which showed a dramatic decrease in contour length of relaxed plasmid molecules upon platination (see Figure 6 below). 

The Mycoplasma Genome The complete genome of the simplest bacterium known, Mycoplasma genitalium, is a circular DNA molecule with 580,070 bp. Calculate the molecular weight and contour length (when relaxed) of this molecule. What is Lko, for the Mycoplasma chromosome If tr = -0.06, what is Lk1... 

According to the Doi-Edwards theory, after time t = Teq following a step deformation at t = 0, the stress relaxation is described by Eqs. (8.52)-(8.56). In obtaining these equations, it is assumed that the primitive-chain contour length is fixed at its equilibrium value at all times. And the curvilinear diffusion of the primitive chain relaxes momentarily the orientational anisotropy (as expressed in terms of the unit vector u(s,t) = 5R(s,t)/9s), or the stress anisotropy, on the portion of the tube that is reached by either of the two chain ends. The theory based on these assumptions, namely, the Doi-Edwards theory, is called the pure reptational chain model. In reality, the primitive-chain contour length should not be fixed, but rather fluctuates (stretches and shrinks) because of thermal (Brownian) motions of the segments. 

While considering the thermal motions of the segments, the stretch-and-shrink motion of the primitive-chain contour length will help relax the tube stress at both ends of the tube. This effect occurs because when a chain moves out of the tube due to a stretching of the contour length following a... 

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