Stress-strain behavior and configurational properties

The persistence length a measures the correlation in the orientation of successive monomers as we move along a polymer chain. One useful definition which is easily apphed to the polyethylene model used here is  

The above equations imply that a can only be obtained accurately from an asymptotic limit. Recent work suggests that this limit is only reached when k 1000 for the polyethylene PE I model and an accurate result cannot be achieved with only small samples. Nevertheless correlation lengths can be deduced from averages over five configurations for values of k up to 100 (these are referred to as aioo) and it is reasonable to assume that to a good approximation the ratios of these values reflect the ratios of the true persistence lengths. 

A set of molecular dynamics simulations was carried out on samples prepared using the direct method described in Section 5.4. In all, four different sample sets of polymer glass were produced by using different preparation procedures. All of the samples were relaxed at 200 K with P = 1 bar for 1 ns. The final densities were all the same to within 1% and we expect all of the samples to have glass transformations in the range 300-400 K on the simulation time scale. The associated correlation lengths and fractions of trans conformers obtained from the final 200 ps of these runs are shown in Table 5.1. 

Sample set A was formed by cooling from the melt as described in Section 5.4. Set B was produced by growing chains at 200 K using PCG and relaxing them for 1 ns at the same temperature. Set C was obtained by flash heat treatment of set B this involves raising the temperature instantaneously to lOOOK for 100 ps followed by rapid cooling back to 200 K. This was not sufficiently drastic to alter the overall configuration of the chain but it did allow conformational transitions to occur and the overall result of this treatment is a net decrease in the trans fraction. As shown in Fig. 5.12 the 

Sample set D was obtained by phantom chain growth at 200 K with the torsional and 1-5 interaction potentials scaled down by a factor of 50 this has the effect of increasing the gauche fraction and produces a highly coiled chain. Van der Waals interactions were then introduced and subsequent relaxation with the full interaction potentials produced a polymer glass with a much reduced fraction of trans states. 

---