Reptative motion

Firstly, the essential correctness of the tube picture has only recently been established in a remarkable series of experiments. The complex monomer diffusive self-correlation predicted has now been seen in field-gradient NMR. Reptative motion across an interface was the only successful explanation of time-resolved neutron reflectivity. Neutron Spin Echo (NSE) can now be extended in time sufficiently to identify the tube diameter directly. A series of massive many-chain numerical simulations have shown tube-like constraints with sizes identical to those obtained by rheology via the plateau modulus Go and NSE). 

We propose here a model which incorporates both reptative motions and fluctuations in length of the occupied path. Part m offers a simple ext ision to include also the effect of finite lifetimes of constraints in polymer liquids. Other woricers have proposed alter-... 

Fig. 6.11. Reptation model Decomposition of the tube resulting from a reptative motion of the primitive chain. The parts which are left empty disappear...

Fig. 6.13. Series of images of a fluorescently stained DNA chain embedded in a concentrated solution of unstained chains Initial conformation (left) partial stretching by a rapid move of the bead at one end (second from the left) chain recoil by a reptative motion in the tube (subsequent pictures to the right). Reprinted with permission from T.Perkins, D.E.Smith and S.Chu. Science 264 819, 1994. Copyright (1994) American Association for the Advancement of Science...

This clear departure from the sieving relation has been interpreted as a signature of reptative motion by Lerman and Frisch.29 This relation also implies that very large molecules should have negligible mobilities, although the decrease is predicted to be slower than in the Rodbard and Chrambach theory. In fact, molecules with have a finite mobility according to this equation, which means that the molecules have to deform enormously in order to move through the pores of the gel. 

Figure 4.11 (a) Schematic representation of a flexible polymer chain with a reptative motion in an environment where other chains (denoted by dots) are assnmed to lie perpendicnlar to the chain, (b) The tube model describing the motion of a flexible polymer chain, represented by the primitive chain, which is assumed to diffuse (i.e., undergo Brownian motion) inside a fictitious tube that consists of Z tube segments of length a. 

Basically, there are four relaxation processes involved. The first is associated with fast relaxation and describes the Rouse motion of a polymer chain between two adjacent entanglement points, and the second is associated with slow relaxation and describes the reptative motion of a polymer chain. In explaining experimental results obtained for the stress relaxation after the imposition of shear deformation, Lin (1986) proposed the following expression for the stress relaxation modulus G(t) ... 

A polymer chain with repulsive interactions between the segments confined into a cylindrical pore has been studied by Monte Carlo simulations by Milchev et al. [115]. Besides the equilibrium conformation of the molecules in the confined geometry, the time-dependent mean-square displacements of the segments was also studied. It is shown fliat relaxation times scaling with hP- as well as hP play a role in the reptative motion of the chain in these tubes. 

If the test chain is infinite, the free energy of the polymer solution is invariant by translation of the chain along itself, the effect of excluded volume is, therefore, very different for motions parallel to the chain or transverse to it this is the origin of a reptative motion. The reptation diffusion coefficient is obtained if the entanglement parameter ij/, proportional to the number of blobs per chain, is larger than a critical value at low values of this parameter the self-diffusion constant is given by a Rouse approximation. 

So far, we have considered only the reptative motion of the test chains, assuming that their environment is frozen.This pure reptation model should, therefore, be applied either to the motion of a linear chain in a gel or to the motions of a short chain in a matrix of infinite chains. If the test chain is embedded in a matrix of chains of the same length, then during the reptation motion the neighboring chains which build the tube also move and the tube is partially renewed. This tube renewal process, also called constraint release, should thus increase the self-diffusion... 

Branching also plays a major role in the dynamics of semi-dilute solutions. The side branches prevent any reptative motion and the motion is considerably slower than that of a linear chain. This has been studied in detail only for star polymers. " Similar problems exist with the reptation of cyclic polymers. 

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