Self-consistent field theory of polymer-ionic molecule complexation

A self-consistent field theory is developed for polymers that are capable of binding small ionic molecules (adsorbates). The polymer-ionic molecule association is described by Ising-like binding variables, C_(i)^(a)(kΔ)(= 0 or 1), whose average determines the number of adsorbed molecules, nBI. Polymer gelation can occur through polymer-ionic molecule complexation in our model. For polymer-polymer cross-links through the ionic molecules, three types of solutions for nBI are obtained, depending on the equilibrium constant of single-ion binding. Spinodal lines calculated from the mean-field free energy exhibit closed-loop regions where the homogeneous phase becomes unstable. This phase instability is driven by the excluded-volume interaction due to the single occupancy of ion-binding sites on the polymers. Moreover, sol-gel transitions are examined using a critical degree of conversion. A gel phase is induced when the concentration of adsorbates is increased. At a higher concentration of the adsorbates, however, a re-entrance from a gel phase into a sol phase arises from the correlation between unoccupied and occupied ion-binding sites. The theory is applied to a model system, poly(vinyl alcohol) and borate ion in aqueous solution with sodium chloride. Good agreement between theory and experiment is obtaine

Phase Separation Induced by Ladder-Like Polymer-Polymer Complexation

Polymer-polymer complexation in solvent is studied using an extension of the self-consistent field theory. The model polymers are capable of forming ladder-like duplex structures. The duplex formation occurs with an abrupt change of entropy, resulting in a first-order transition. Moreover, the complexation can be stabilized by solvent-polymer interactions, instead of the usual specific binding interactions. Various types of unconventional phase diagrams are predicted. For example, phase separation with decreasing χ-parameter between duplex polymer and solvent can be induced, leading to a lower critical solution temperature (LCST) behavior. Multiphase coexistence points at which two, three, or four phases coexist are also obtained. Under certain conditions a homogeneous phase becomes unstable when the polymer chain length is decreased, in contrast to the standard Flory-Huggins theory

Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure