The Landau–de Gennes free energy expansion of a melt of V-shaped polymer molecules

Abstract

The phase behavior of a monodisperse melt of polymer molecules consisting of two rod-like segments joined at an angle α has been inspected within the Landau theory of phase transitions. The interactions between monomer units were assumed to be of the Maier-Saupe form. The Landau-de Gennes expansion of the free energy of the melt has been obtained up to the sixth order in powers of the nematic order parameter, the coefficients of this expansion have been calculated from the microscopic model of polymer molecule. The phase diagram contains the regions of stability of isotropic, prolate uniaxial, oblate uniaxial, and biaxial nematic phases. The isotropic-uniaxial nematic and uniaxial-biaxial nematic transitions are of the first and second order, respectively. We found two Landau points in the phase diagram at which continuous transition from biaxial nematic state to isotropic phase occurs.

Molecular Considerations for Mesophase Interaction and Alignment of Lyotropic Liquid Crystalline Semiconducting Polymers

“…These lyotropic mesophases consist of extended polymer chains partaking in crystalline π-stacking in solution, forming elongated crystallites typical of nematic mesophases due to the highly anisotropic nature of the π–π interactions on rigid conjugated polymers. At the transition from isotropic to nematic solution, Maier–Saupe theory describes how the entropic loss due to short-range orientational ordering is countered by anisotropic attractive interactions. − These interactions are analogous to the Flory–Huggins interaction parameter, having the form μ N ∼ A / T + B where A is the interaction parameter; T is the nematic–isotropic clearing temperature; and B captures disagreements between the small molecule and polymeric forms of the Maier–Saupe interaction parameters, possibly due to entropic effects . The Maier–Saupe parameter can be quantified in polymeric systems by measuring the nematic–isotropic clearing temperature and the molecular weight ( N ).…”

“…The effects these structural changes have on intermolecular backbone attraction are estimated using dynamic scanning calorimetry (DSC) and grazing incidence wide-angle X-ray scattering (GIWAXS). For liquid crystals, the Maier–Saupe interaction parameter (μ) describes how the entropic cost of short-range orientational order balances enthalpic gains due to anisotropic intermolecular attraction at the isotropic–nematic transition and is used to compare intermolecular interactions in rodlike polymers. − …”