Self-consistent-field method lengths

Consider, as an example, polyethylene if the chains are packed as in the crystal (Fig. 1), there are 5.5 x 10 per m in the plane perpendicular to their length. Hence the tensile fracture stress would be 33 GPa. Variants of this approach, using simple Morse potentials, provide values ranging from about 19 to 36 GPa. Other calculations using Hartree-Fock self-consistent field methods yield values of 66 GPa at 0 K (Crist et al., 1979). This last value seems a bit high and may be due to inaccuracies of the Hartree-Fock approximation at large atomic separations. 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

To summarize, the example of homopolymer/copolymer mixtmes demonstrates nicely how field-theoretic simulations can be used to study non-trivial fluctuation effects in polymer blends within the Gaussian chain model The main advantage of these simulations is that they can be combined in a natural way with standard self-consistent field calculations. As mentioned earlier, the self-consistent field theory is one of the most powerful methods for the theoretical description of polymer blends, and it is often accurate on a quantitative level hi many regions of the parameter space, fluctuations are irrelevant for large chain lengths (large Jf) and simulations are not necessary. Field-theoretic simulations are well suited to complement self-consistent field theories in those parameter regions where fluctuation effects become important. 

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