Dynamics reptation

The scaling dependence of the diffusion coefficient on N and Cobs Iso poses a number of questions. While the original scaling predictions, based on reptation dynamics [26,38], oc N, have been verified by some measurements [91,98], significant discrepancies have been reported too [95,96]. Attempts to interpret existing data in terms of alternative models, e.g., by the so-called hydrodynamic scaling model [96], fail to describe observations [100,101]. 

K. Kremer, G. Grest, I. Carmesin. Crossover from Rouse to reptation dynamics. Phys Rev Lett 61 566-569, 1988. 

Table 2. Dynamic structure factors for reptational dynamics...

Fig. 2.48 Self-diffusion of nearly symmetric diblock copolymers measured using forced Rayleigh scattering (Dalvi et al. 1993). (a) Diffusivities, D, for the lower molecular weight PS-PVP sample, which is disordered at these temperatures, have been scaled down by a factor of 0.48, assumming Rouse dynamics (b) D for the lower molecular weight symmetric PEP-PEE diblock copolymer have been scaled down by a factor of 0.40, assuming reptation dynamics. The solid line indicates a fit of the standard Williams-Landel-Ferry (WLF) temperature dependence to the data for the lower molecular weight sample. Values of M are in g mol1.

The Doi-Edwards, reptation based model makes specific predictions for the relaxation dynamics of different portions of a polymer chain. Specifically, the relaxation of the chain ends is predicted to be substantially faster than the relaxation of the center. This is a result of the reptation dynamics, which have the ends first leaving the confines of the tube. Using polymer chains that were selectively deuterated either at the ends or at the middle, Ylitalo and coworkers [135] examined this problem and found that the Doi-Edwards model was able to successfully predict the observed behavior once the effects of orientational coupling was included. The same group further explored the phenomena of orientational coupling in papers that focused on its molecular weight [136] and temperature [137]... 

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

Both the questions of the transition from Rouse to reptation dynamics and of what fixes the average distance between entanglements in polymer liquids has been the subject of a number of recent theoretical and experimental investigations. 

Reptation Dynamics Viscosity and Steady-State Compliance for... 

Tube length fluctuations modify the rheological response of entangled polymers. Reptation dynamics adds a regime to the mean-square monomer displacement that was not present in the free Rouse model. This extra regime is a characteristic signature of Rouse motion of a chain confined to a tube. 

Roby and Joanny [27] improved the model of Benmouna, et al. [23] by incorporating interchain hydrodynamic interactions. At elevated concentrations, reptation dynamics were assumed, approximating the solution as a polymer melt in which mesoscopic polymer-solvent blobs are effective monomers. Hammouda [28] repeated the calculation, removing the restriction that the system contained equal amounts of two species having the same molecular weight, and analyzing tagged-tracer experiments. 

The molecular aspects of interdiffusion of linear entangled polymers (M > Me) during welding of polymer interfaces are summarized in Table 1 [1]. The reptation dynamics and the interface structure relations in Table 1 have been... 

Stochastic equation for reptation dynamics Although the above probabilistic description is quite useful in understanding the essence of reptation dynamics, it becomes progressively more difficult to proceed with the calculation for other types of time correlation function. For example, it is not easy to calculate the mean square displacement of a primitive chain segment (R(s, t)-R(s, 0)) ) by this method. In this section we shall describe a convenient method" for calculating general time correlation functions. 

First we derive a simple mathematical equation for reptation dynamics. Let A (0 be the distance that the primitive chain moves in a time interval between t and t + Ar, then... 

Theoretical calculations of the scattering intensity based on the reptation dynamics are given in refs 81-83. 

We shall now derive the constitutive equation for reptation dynamics. To simplify the analysis, we assume that tiie contour length of the primitive chain remains at the equilibrium value L under macroscopic deformation (inextensible primitive chain). This assumption is valid if the characteristic magnitude of the velocity gradient is much less than 1/Tj, i.e. 

In the reptation dynamics model, proposed by de Gennes and Edwards, " individual polymer chains are conjectured to move like Brownian snakes in a field (tube) of topological constraints imposed by entanglements from neighbouring chains, (Fig. 1) at f = 0. At time h, some end portions of the chain (these are called the minor chains ) have already escaped from the initial tube by reptation. 

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