  To describe the interaction between longitudinal density modulations along
collagen fibrils (the D-band) with the radial twist-field of molecular
orientation (double-twist), we couple phase-field-crystal (PFC) with
liquid-crystalline free-energies to obtain a hybrid model of equilibrium
collagen fibril structure. We numerically compute the resulting axial and
radial structure. We find two distinct fibrillar phases, `L' and `C', with a
coexistence line that ends in an Ising-like critical point. We propose that
coexistence between these phases can explain the bimodal distribution of fibril
radii that has been widely reported within tendon tissues. Tensile strain
applied to our model fibrils straightens the average fibrillar twist and
flattens the D-band modulation. Our PFC approach should apply directly to other
longitudinally-modulated chiral filaments, such as fibrin and intermediate
filaments.
