The Orofino-Flory (OF) type smoothed-density theories for the end-distance expansion factor ~R and the second virial coefficient Az of flexible chains with three-segment interactions are inconsistent with first-order perturbation calculations unless the ternary cluster integral fla is zero. It is shown in the present paper that the inconsistency arises from the factorization approximation to segment density distribution functions invoked in the smoothed-density model and that a proper treatment of such functions leads to expressions consistent with the perturbation calculations but different from the OF type equations. Thus, for non-zero [/3 and near the ® point the previous smoothed-density or mean-field theories retain no valid place, even though those for A2 account for a few experimental findings (at or below the ® temperature) that two-parameter theories fail to explain. In particular, the prediction of a coil-globule transition by the OF type equations has no theoretical significance. It is also shown by a perturbation calculation that when both binary and ternary cluster integrals are vanishingly small, ~R for an infinitely long chain is expressed in terms of a single excluded-volume variable up to second order in f13 with the same numerical coefficients as those in the two-parameter theory.
Посилання на статтю:
Remarks on smoothed-density theories for flexible chains with three-segment interactions / Takashi Norisuye* and Yo Nakamura // Polymer. – 1993. – Vol 34. – P. 1440-1443.