Continuous unperturbed chains

Continuous Unperturbed Chains via Fast Monte Carlo.255... 

The initial configuration for aU single unperturbed chain simulations was all-trans, from which the conformation quickly departed. After permitting the chain to explore a sufficient number ( 200 million) of its configurations, statistics were accumulated for the properties of interest We will refer to the chains sampled by this method as continuous unperturbed chains (CUC). Due to the simplicity of the sampling method and the local nature of the unperturbed... 

Fig. 7. Running average erf the squared end-to-end distance vs Monte Carlo c les for the chain that initially had the largest end-to-end distance and for the chain that initially had the smallest end-to-oid distance in a 10-chain 78-mer ( polyethylene ) system at 450K and Oil MPa. The horizontal line shows the value for continuous unperturbed chains...

Fig. 9a, b. Intra-chain pair density function radial distance a dotted curve result of bulk NPT Monte Carlo simulation of a 32-chain 24-mer (n-tetracosane) system at 450 K and 0.1 MPa dashed curve result from fast sampling of continuous unperturbed chains curves are neatly identical b dotted curve result from bulk NPT Monte Carlo simulation of a 10-chain 78-mer ( polyethylene ) system at 450 K and 0.1 MPa dashed curve result from fast sampling of continuous unperturbed chains... 

Fig. IOl Probability distribution of torsion angle idative to trans, (< > — 4>(t)). SoM curve, result of bulk NPT Monte Carlo simulation of a 32-drain 24-mer (n-tetiaoisane) syston at 450 K and 0.1 MPa. Dashed curve, result of Cast sanq>lii% rtf continuous unperturbed chains. Oirves are neaity idmtical...

The two PRISM predictions are shown in Fig. 1 la as dashed and dotted curves. We can see there that both PRISM predictions are almost indistinguishable from each other as a result of the to(r) from the bulk NPT simulation and from the continuous unperturbed chains being almost indistinguishable. However, both PRISM predictions are definitely distinguishable from the exact results from the NPT MC simulation. At small r, the PRISM prediction for g(r) rises more rapidly than the exact g(r), resulting in a bulging shape PRISM also underpredicts the first peak. 

Thus, with the fast sampling of continuous unperturbed chains, we are able to capture in great detail the characteristics of chairs in the bulk NPT simulation for the R-tetracosane system. Before extending the comparison to long-chain systems, we examine the orientational ordering of bonds, quantified using... 

Fig. 16. Plot of the mean uared radius of gyration vs Monte Carlo cycles for an NPT Monte Carlo of 78-mer ( polyethjfcne ) system at 450 K and (XI MPa. The value from the sanqdiiig of continuous unperturbed chains is 219J2...

The evolution of in the superbox system is shown in Fig. 16. The values of are substantially larger than those of the 10-chain system but still short of the value for the continuous unperturbed chains again, they show very little tendency to change away from the initial configuration. The autocorrelation function of the end-to-end unit vectors of the chains showed similar slow decay... 

In addition to the bulk simulation studies we have also developed a fast and efficient method of generating continuous unperturbed chains. This method is 300 times faster than the bulk MC simulation method. Comparisons between our bulk MC results and continuum unperturbed chains allowed for a direct test of the Flory random coil hypothesis. In those bulk MC simulations that equilibrate conformadonally, chains in the melt were found to be indistinguishable from continuous unperturbed chains to an excellent approximation at all length scales. 

The intra-chain pair density functions obtained from both the bulk simulation and the continuous unperturbed chains were used as input to the polymer-RISM integral equation for estimating the intermolecular pair distribution function g(r) (using a soft-Percus Yevick closure). We found that PRISM underpredicts the first peak in g(r), while also overpredicting the steefmess of the rise to the first peak. 

---