Molecular modelling procedures have been used to determine statistical parameters of isolated chains, with the objective of achieving a simple description which defines the tendency of a molecule to form a liquid-crystalline phase, its mesogenicity. Initial attention is focused on the persistence length parameter as the most promising in this context, while a related parameter, the turn-round length, is introduced to provide a description of mesogenicity which is equally applicable to molecules which consist of rigid segments separated by flexible sequences. A range of known mesogenic molecules has been modelled using Monte Carlo routines based on carefully determined bond-rotation potentials. For each molecule type a large number of chains are built for each temperature, and the chain parameters determined as averages over the models. Evidence is presented to suggest that for liquid-crystalline polymer molecules other than those containing flexible sequences, the nematic to isotropic transition temperature occurs when the ratio of the persistence length to diameter (the persistence ratio) reaches a value of 5. The predictive possibilities of this criterion are explored in the estimation of the nematic-isotropic transition temperatures of one or two common mesogenic polymers which are too high to be accessed experimentally. It is also applied to polyethylene, giving a value of 150 K for the onset of liquid crystallinity, a transition which is of course not normally seen owing to crystallization. Modelling of a series of aromatic copolyesters which contain different lengths of flexible (alkane) sequences, shows that the critical persistence ratio, calculated at the experimentally observed transition temperature, drops from 5 to 2.5 when the flexible sequences are long enough to decouple the orientation of neighbouring rod segments, and form comparatively low-energy hairpin folds in the mesophase. The introduction of the turn-round length/diameter parameter is promising and appears to have a true predictive capability to cover series of molecules ranging from worm-like to jointed rigid rod (Kuhn)-like.
We synthesized a series of poly(dialkyl 1-viny-3,5isophthalate) (P 3,5 -n, n is the number of carbons on alkyl group, n = 4−18), wherein the polyethylene backbone is jacketed by the isophthalate side chains. The phase behaviors of P 3,5 -n were investigated by using various techniques including thermal analysis, polarized light microscopy, and X-ray diffraction. It is identified that with n ≥ 8 the P 3,5 -n samples form the hexagonal columnar phase (Φ H ). Furthermore, P 3,5 -16 and P 3,5 -18 can exhibit a four-column hexagonal superlattice (Φ H S ), wherein one column is frustrated. After the alkyl tails are fully melted or crystallized, the Φ H S degrades into the conventional Φ H phase. For the Φ H of P 3,5 -n observed, the cross section area of the column (S) increases linearly with n, S = 1.97 + 0.52n (nm 2 ). The number of repeating units (Z rep ) required to be packed in the 0.44 nm thick column stratum is 4. Compared with poly(dialkyl 1-vinyl-2,5-terephthalate) (P 2,5 -n), which is the isomer of P 3,5 -n and can form the Φ H phase based on the parallel packing of a "single-chain column", P 3,5 -n possesses the intercept and slope of the linear function of S vs n and the Z rep value nearly twice that found for P 2,5 -n. We propose that P 3,5 -n can self-organize into the column containing two chains laterally associated together. Namely, P 3,5 -n takes the "double-chain column" rather than the "single-chain column" as the building block for the Φ H phase.
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