Reptation technique

The reptation technique consists of starting with a configuration of a linear chain, then randomly removing one end segment and adding it to the other end. The new orientation of the segment is random, and it is accepted only if the excluded volume condition is preserved. 

In analogy to reptation techniques, it relies on a high concentration of chain ends. It becomes inefficient when long chains in dense systems are considered. 

The simulations in Ref. 22 were performed using the UA approximation (see above) with the methods and the force field already described. The same 6-12 potential was used for the mutual interactions of the methyl and methylene groups and for their interactions with the atomic units comprising the solid surfaces. A total of 1297 tridecane molecules was introduced in the basic cell one at a time in such a way that two nonbonded units (including those of the solid surfaces) could not come within 0.32 run from each other. The system was then equilibrated at 300 K using the reptation technique. The results shown in the next sections represent the average over 10 different equilibrium models obtained in sequence and separated by more than 800000 accepted reptations. It was verified that the tridecane molecules were able to diffuse during the simulation from the narrow slits to the wider slits and vice versa. 

For very large biopolymer molecules (e.g., DNAs over 30 x 106 molecular weight), the polymeric chain orients with the field and snakes (reptates) through the gel. In this way the sieving effect is rendered ineffective it can be restored by switching back and forth between fields oriented at different angles in a technique called pulsed field gel electrophoresis, or PFGE [29,30]. 

This reptation Monte Carlo algorithm has been incorporated into the NRCC program CLAMPS. Significant chain motions are effectuated by these single moves (17). We have employed this technique to sample the Boltzmann distribution of our polymer systems. 

Synthetic polyelectrolytes can be separated by capillary electrophoresis applying the same rules derived for the electrophoresis of biopolymers. In the reptation regime, determination of the molecular mass and polydispersity of the polyelectrolytes is possible. Introduction of chromophores facilitates the detection of non-UV-absorbing polymers. Indirect detection techniques can probably be applied when analytes and chromophores of similar mobilities are available. 

High-resolution proton DQ MAS NMR is used as a new technique that is capable of revealing complex motional processes in entangled polymer melts. Theoretical analysis shows the connection of quantities relating anisotropic polymer dynamics to data obtained from our DQ-MAS NMR experiment. With this technique, dynamic chain ordering as well as scaling laws consistent with the reptation model was previously observed for polybutadiene (PB). 

Among the major developments are a new approach to long-range relaxational motions known as the theory of reptation, and the further elucidation of the kinetic theory of rubber elasticity. In this second edition, we have attempted to take account of some of these developments on a level consistent with the introductory nature of the text. We have also added an entirely new chapter on dielectric relaxation, a technique now widely used to investigate molecular motions in polar polymers. Finally, we have tried to strengthen and clarify several other sections as well as eliminate errors or inconsistencies in the first edition that have been pointed out to us by colleagues and students. 

Simulation techniques for on- or off-lattice systems are, in general, applicable to systems with different degrees of coarsening. Their effectiveness, however, is often model-specific. In the following sections we describe different types of moves some of them can be applied to almost any type of molecular model (e.g., reptation, configurational-bias), and some others are applicable only to certain types of models (e.g., extended configurational bias or concerted-rotations). 

De Gennes (1971) postulated that polymer molecules were constrained to move along a tube formed by neighbouring molecules. In a deformed melt, the ends of the molecules could escape from the tube by a reciprocating motion (reptation), whereas the centre of the molecule was trapped in the tube. When the chain end advanced, it chose from a number of different paths in the melt. This theory predicts that the zero-shear rate viscosity depends on the cube of the molecular weight. However, in the absence of techniques to image the motion of single polymer molecules in a melt, it is hard to confirm the theory. 

There seem to be two factors at play. First, many of the experiments on latex films involve samples with a broad molar mass distribution. The distribution of diffusion coefficients broadens the concentration profile at the interface so that the measurements become insensitive to the difference between the two diffusion mechanisms. Second, in the experiments employing emulsified particles comprising essentially monodisperse PS, where reptation effects should be most pronounced, the SANS technique is less sensitive to early-time diffusion than DET. In the SANS experiment, one monitors the consequences of the increase in radius of gyration of the labelled particles. Reptation effects should be most prominent when changes in the radius are small. In contrast, DET experiments are sensitive to volume of mixing. Small increases in the radius of a donor-labelled particle correspond to large changes in or No DET experiments have been reported for polymer particles of narrow molar mass distribution, and so the prediction that DEX experiments should be more sensitive than SANS experiments to reptation effects remains untested. 

Panagiotopoulos and coworkers [51] use the same parameters as Larson for the study of phase behavior, but with two different simulation methodologies. The first technique is the Gibbs ensemble method, in which each bulk phase is simulated in a separate cell and molecules are interchanged and volumes adjusted between the two for equilibration of the system [52]. The second is a standard canonical ensemble simulation, like Larson s, but employs the configurational bias Monte Carlo method. The configurational bias Monte Carlo method is much more efficient than the ones based on reptation and other local moves but is not useful if any dynamic information is sought from the simulations. 

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