Good- and bad-solvent effect on the rotational statistics of a long chain molecule

摘要

The long-range solvent-mediated intramolecular forces that may either expand or contract a polymer chain, may also change the probabilities of the rotational states (trans and gauche in a polyethylene chain). This effect is calculated in the present paper, using the chain self-consistent free energy optimisation approach, within the Gaussian assumption, and following the rotational-isomeric-state approximation with neighbour interaction; representation of the chain configuration in terms of Fourier normal modes proves to be a most important feature of the algorithm. Except under a very high expansion, the relative change of the rotational probabilities is a function of the reduced temperature τ = (T - Θ)/T, instead of τN~(1/2) as it happens with the chain dimensions (N = molecular length). The statistical distribution of the additional, or excess rotational probabilities is markedly non-Markoffian. In the poor-solvent case leading to chain contraction the excess rotational states are very far apart along the chain sequence, whereas in a good solvent they are clustered within chain strands consisting of no more than k-bar approx= 15 chain bonds (at T = 400 K for polyethylene), separated by unperturbed strands whose length is no less than k bonds. The value of k is roughly proportional to the number of bonds comprised within the chain persistence length. Although small, the γ effect on the NMR ~13C chemical shift depending on the change of the relative amount of trans and gauche rotational states, produced by a good solvent, should be measurable under appropriate conditions.