The largest eigenvalue method for stereo-regular vinyl chains

We derived the analytical solution of the eigenvalue problem for stereo-regular vinyl chains, such as stereo-regular polypropylene chains. The solution is applicable to all stereo-regular polymers of the type (AB)_x which do not have symmetry between gauche⁺ and gauche⁻ states, and to polymers, such as polyoxymethylene or polydimethylsiloxane, for which symmetry between the gauche⁺ and gauche⁻ states does exist. For symmetric chains, the general solution of the eigenvalue problem is reduced to the known solution for polyoxymethylene chains. To illustrate the method the calculations have been performed for the three rotational states (trans, gauche⁺ and gauche⁻) model, but the general algebraic solution is applicable for any ν rotational states models of polymer chains. We used the analytical solution of the eigenvalue problem to calculate numerically elastic properties of stereo-regular polypropylene chains within the framework of Mark-Curro theory (J Chem Phys, 79, 5705, 1983).