Phase Behavior of Ternary Systems Involving a Conformationally Variable Chain and a Randomly Coiled Polymer

Abstract

Ternary systems consisting of a conformationally variable chain capable of assuming either a rodlike helix or a random coil conformation, a randomly coiled polymer, and a solvent were treated according to the lattice model proposed by Flory. The partition function has been derived in consideration of the Flory−Matheson expression related to the free energy contribution from the chain conformation changes. A marked increase of the miscible isotropic zone was predicted when the chain rigidity of the conformationally variable polymer in the isotropic phase is reduced. The conformationally variable chain tends to adopt a rodlike form as long as it enters the anisotropic phase in which the randomly coiled polymer is essentially excluded. The influence of various molecular structure parameters, solvent−polymer interaction, and temperature was also studied.

Phase Behavior of Ternary Systems Involving a Conformationally Variable Chain and a Randomly Coiled Polymer: Effect of External Orientational Field

“…The minimum value of −ln Z M is located at θ = 1 for all the parameters examined. Including the energy term of the external orientational field does not change the general feature of the dependence of −ln Z M on θ as reported in our previous work . In the anisotropic phase, the maximum stability occurs at θ = 1.…”

“…The 〈cos 2 Ψ j 〉 term is also equal to 1 / 3 due to the random orientations. , Therefore, the last term of eq 2 appears to be −ε 0 n 2 x 2 /3. Incorporating this result, together with the conditions obtained for the isotropy according to ref , into eq 2 gives …”

“…Under such a circumstance, the last term of eq 2, which is contributed from the external orientational field, reduces to −ε 0 n 2 x 2 〈cos 2 Ψ i 〉. With further substituting the conditions for the anisotropy as specified in ref , eq 2 becomes …”

“…If the ternary system is subjected to an external field, an extra term as expressed by eq 1 should be included in the lattice scheme. After incorporating eq 1, the mixing free energy expression for an athermal ternary system in the presence of the external field becomes where n 1 , n 2 , and n 3 are the numbers of the solvent, polypeptide, and coiled polymer with lengths of 1, x 2 , and x 3 , respectively, x̄ is the number-average of x 2 and x 3 , v 1 , v 2 , and v 3 represent the volume fractions of the corresponding components, n 0 and n p equal ( n 1 + x 2 n 2 + x 3 n 3 ) and ( n 2 + n 3 ), respectively, s and σ denote respectively the statistical weight for a unit in the helical state relative to the coil and the weighting factor for initiation of a helical sequence, m represents the number of repeat units (i.e., peptide residues) in the lattice segment, ρ is the fraction of units that mark the beginning of a helical sequence, β is a Lagrangian multiplier, and Q and S 0 are orientation-related quantities that have been defined in ref .…”

“…Theoretical extension for the ternary solutions which contain a rigid-rod solute with flexible side chains, a randomly coiled polymer, and a solvent was reported by Ballauff , and Inomata et al , It has been found that the presence of the flexible side chains could enhance the miscibility between the rodlike and coiled polymers in both isotropic and anisotropic phases. Polymer chain conformation changes in the isotropic−anisotropic transition present an important issue associated with the phase behavior, and they may pertain to semirigid macromolecules in general. − Recently, Lin et al have analyzed the effect of the chain conformation variation of the mesogenic polymer on the phase diagrams of the ternary systems . The conformationally variable chain is exemplified by polypeptide in which each unit is able to assume either a helix or a random coil form.…”