Structural parameters of twist-bend nematics and splay-bend nematics in Dozov's theory

This paper presents the results of numerical calculations revealing how the structural parameters (i.e., the pitch pTB, the spatial period pSB, and the tilt angle θTB or θSB) of twist-bend nematics (NTB) and splay-bend nematics (NSB) depend on the values of elastic constants in Dozov's theory [I. Dozov, Europhys. Lett. 56, 247 (2001)]. Alternative formulas for pTB, θTB, pSB, and θSB have been derived and it has been proved that they give more accurate results than the expressions proposed by Dozov. Although the determination of the fourth-order elastic constants C₁, C₂, and C₃ is not feasible in a simple way, the order of magnitude of the sum C₁+C₂ has been easily estimated and is equal to 10^-314pt0exJ4pt0exm. Moreover, the numerical calculations have shown that twist-bend nematics can exist even when K₁₁ is smaller than 2K₂₂ and thus Dozov's criterion K₁₁>2K₂₂ for the stability of the NTB phase is not strictly satisfied.