Conformational statistics of semiflexible polymers: comparison between different models

Recently performed small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) experiments (Macromolecules 30 (1997) 273) had provided experimental data for measurement of the static scattering formfactor which are in very good agreement with the theoretical results for the formfactor obtained with the help of the Dirac model of semiflexible polymer chains. This agreement had prompted us to make additional detailed comparisons between the observables which can be calculated with help of the Dirac and the Kratky–Porod (K-P) models of semiflexible chains. In this work we provide comparison between the closed form exact analytic results for the Dirac formfactor and various approximations of the static formfactor obtained with help of the K-P model. Remarkable agreement between the exact result and various approximations is thoroughly investigated through systematic classical and semiclassical analysis of the K-P model. We found conditions (approximations) under which the K-P model could be obtained from the Dirac model. This enabled us to calculate the observables related to measurements of optical anisotropy and magnetic birefringence and to reanalyze previously obtained exact analytic results for the force–extension relations based on the Dirac model.