Flory-Vrij analysis

Figure 2 shows that, for all but the shortest chains, the Flory-Vrij analysis predicts a slightly higher melting temperature than the present mean-field model. Both approximations are give values higher than the simulation results, but the overall agreement is reasonable. 

Fig.2 Melting temperatures of polymers (faTm/Ec) with variable chain lengths. The solid line is calculated from Eq. 10, the dashed line is calculated from Flory-Vrij analysis (Eq. 11), and the circles are the simulation results in the optimized approach. In simulations, the occupation density is 0.9375, and the linear size of the cubic box is set to 32 for short chains and 64 for long chains (Hu and Frenkel, unpublished results)...

Fig. 2.12 Melting temperature of n-alkanes as a function of chain length. Solid curve calculated from Flory-Vrij analysis.(l) Experimental results Ungar etal. (13) o Flory and Vrij (11), Lee and Wegner (14) Takamizawa et al. (28).

Fig. 2.18 Plot of melting temperature as a function of the number of carbon atoms in chain. Curve A Flory-Vrij analysis. Curves B and C theoretical calculations for disordered end sequences with = 1200 and 4600 respectively. values for n-parafflns.(l)...

Figure 13 Melting temperatures of n>alkanes as a function of chain length. Solid curve calculated from Flory-Vrij analysis.

Examination of the directly determined melting temperatures makes abundantly clear that proposed equilibrium melting temperatures of 138.1°C and 138.9 C (24)(25) are incompatible with experiment. They obviously should be dismissed. The know experimental facts were apparently overlooked by the investigators. The remainder of the extrapolated Tm° s fall into two groups, one around 142°C and the other about 146°C. On more detailed analysis, the original Flory-Vrij conclusions are found to be strongly favored (32). 

Utilizing the parameters cited, the left-hand side of equation (8) can be calculated for each n-alkane for an assumed value of T. Flory and Vrij found that with the available data the best value of for linear polyethylene was 418.5 K. Another way to assess the validity of the analysis is to directly calculate from equation (8) the melting point of the n-alkanes. The solid line in Figure 12 represents the calculated values of plotted against n for the n-alkanes up to Here,... 

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