A microscopic model of cholesteric polypeptide solutions

2014 A microscopic model of cholesteric polypeptide liquid crystals is proposed Polypeptide molecules may form 03B1-helix conformations. It is assumed that such molecules have uniformly distributed electric dipoles along the long axes of molecules. The directions of the dipoles are assumed to be perpendicular to the long axes and rotate uniformly along the long axes. It is assumed that the mólecules have short range steric interactions and perturbative long range weak dipole-dipole interactions. The free energy of the cholesteric phase is calculated by second order perturbation theory. The cholesteric twist and concentration dependence are calculated. The results have the correct order of magnitude and are in qualitative agreement with experimental observations. J. Physique 43 (1982) 559-565 MARS 1982, Classification Physics Abstracts 34.20B This is a theoretical model to show how a simple helical arrangement of electric dipoles along long axes of rigid linear molecules in solution may produce a cholesteric phase. It is well known that some polypeptides at sufficiently high concentration exhibit a cholesteric mesophase [1]. It is assumed that there is a uniform distribution of dipoles along long axes of the a-helix molecules. The dipoles are perpendicular to the axis and rotate uniformly along the axis forming molecular chirality (Fig. 1). It is assumed that molecules have short range steric interactions which favour a nematic ordering and perturbative long range weak dipole-dipole interactions. In figure 1, q is the wave number of molecular chirality. When q > 0, the chirality of a molecular is right handed, and when q C 0, it is left handed. In figure 2, a sketch of a cholesteric phase is shown. The planes A, B, and C are parallel to the xy plane. The direction of cholesteric twist is parallel to the z axis. Fig. 1. A schematic representation of the arrangement of the dipoles on the long axis of a molecule. Suppose that there is a dipole P1 at the origin. The molecule which includes PI lies on the plane A and makes angle (p with x axis (Fig. 3). Also, consider a dipole P2 at R and the molecule which includes that dipole lies on the plane B. The direction of that molecule is perpendicular to yz plane. The angles a and a2 are coordinates of rotational degree of freedom of molecules with respect to their long axes. The helicity Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004303055900