Intrachain flexibility constraints on phase stabilities and odd-even effects in multiple smectic-Aand nematic liquid crystals

The importance of the flexibility of n-alkyl tail chains in real liquid-crystal systems is reviewed. Two new microscopic, molecular statistical-physics theories (a full statistical theory and a simpler but accurate approximate theory) for the intrachain constraints on the n-alkyl tail-chain flexibility are presented and are compared with each other and with an old, more approximate theory for tail-chain flexibility used in earlier papers. The new approximate approach is computationally much faster than the full statistical method and is the first treatment to generate and explain odd-even effects in multiple smectic-A phases and the first treatment to generate and explain odd-even effects in smectic-A and nematic phases without resorting to ad hoc or arbitrarily adjustable fits to experimental data. Phase stabilities and odd-even effects for various thermodynamic and molecular ordering properties are calculated in the smectic-$A_1$, smectic-$A_d$, and nematic liquid-crystal phases and the isotropic liquid phase using the new approximate method. Some predictions and accompanying physical explanations are made for various systems that have not yet been chemically synthesized and/or experimentally studied. The theoretical results in this paper are in good semiquantitative and (in some cases) quantitative agreement with available experimental data and offer some significant improvements—compared with experiment—over the theoretical results of earlier papers, especially with regard to the relative stabilities of the nematic and multiple smectic-A phases. The calculations in this paper also show for the first time that intrachain constraints on the tail-chain flexibility are by far the major factor responsible for odd-even effects in these liquid-crystal systems.