1.1 Background

Macromolecules are, in principle, flexible entities. They are essentially composed of linear chains of chemical, covalent bonds joining atoms such as carbon, oxygen, nitrogen, etc., to which side groups are usually anchored. The length of the bonds between successive atoms, b, and the angle between consecutive bonds are more or less fixed. All, or at least some of the bonds in the chain skeleton are single (not double or triple), i.e., they are sigma bonds, in the terminology of physical chemistry. Such bonds (unlike double or triple ones) have the remarkable feature of allowing the internal rotation of the neighboring bonds around them. Assuming four consecutive atoms, i, i+1, i+2, and i+3, if we fix atom i, then atom i+1 is fixed by the bond length, and i+2 is fixed by the bond angle. Owing to the internal rotation, or torsion, around the bond joining i+1 and i+2, atom i+3 can rotate on a cone, as illustrated in Figure 1. There is a variety of positions, characterized by the rotational angle, ?. Then, for a given position of atom i+3 there is a variety of positions for atom i+4, and so on. As a consequence, such a molecule is continuously changing from one possible conformation to another, and it therefore behaves like a flexible entity. It is usually regarded...