Random coil

Many unbranched, linear homopolymers — in solution, or above their melting temperatures — assume (approximate) random coils.

So, if each conformation has an equal probability or statistical weight, chains are much more likely to be ball-like than they are to be extended — a purely entropic effect.

A longer, "effective" unit length can be defined such that the chain can be regarded as freely-jointed, along with a smaller N, such that the constraint L = N x l is still obeyed.

The average end-to-end distance for freely-rotating (not freely-jointed) polymethylene (polyethylene with each -C-C- considered as a subunit) is l times the square root of 2N, an increase by a factor of about 1.4.

Unlike the zero volume assumed in a random walk calculation, all real polymers' segments occupy space because of the van der Waals radii of their atoms, including bulky substituent groups that interfere with bond rotations.

Because their polymerization is stochastically driven, chain lengths in any real population of synthetic polymers will obey a statistical distribution.

We may still hope that the ideal-chain, random-coil model will be at least a qualitative indication of the shapes and dimensions of real polymers in solution, and in the amorphous state, as long as there are only weak physicochemical interactions between the monomers.

But there is reason to believe (e.g., neutron diffraction studies) that excluded volume effects may cancel out, so that, under certain conditions, chain dimensions in amorphous polymers have approximately the ideal, calculated size [3] When separate chains interact cooperatively, as in forming crystalline regions in solid thermoplastics, a different mathematical approach must be used.

Stiffer polymers such as helical polypeptides, Kevlar, and double-stranded DNA can be treated by the worm-like chain model.

Even copolymers with monomers of unequal length will distribute in random coils if the subunits lack any specific interactions.

More complex polymers such as proteins, with various interacting chemical groups attached to their backbones, self-assemble into well-defined structures.

But segments of proteins, and polypeptides that lack secondary structure, are often assumed to exhibit a random-coil conformation in which the only fixed relationship is the joining of adjacent amino acid residues by a peptide bond.

This is not actually the case, since the ensemble will be energy weighted due to interactions between amino acid side-chains, with lower-energy conformations being present more frequently.

In addition, even arbitrary sequences of amino acids tend to exhibit some hydrogen bonding and secondary structure.

Furthermore, there are signals in multidimensional NMR experiments that indicate that stable, non-local amino acid interactions are absent for polypeptides in a random-coil conformation.

Likewise, in the images produced by crystallography experiments, segments of random coil result simply in a reduction in "electron density" or contrast.