Achiral helical twisting power

At first glance, the helical twisting power is a property of the dopant itself but it is also strongly influenced by the achiral host phase. The latter effect is due to several reasons. Among these are the elasticity of the host, correlated to the size and shape of the micelles, but also to solubilities and locations of the dopants with respect to the aggregates, see Section 14.2.7. 

Equation (11) of Nordio et al [20] can be generalised to develop a theory with a non-traceless pseudotensor of second rank Wy, the chirality interaction tensor. Because the contribution of the interaction energy from the chiral/chiral potentials of the molecules is small in comparison to the chiral/achiral contribution, the helical twisting power is then given for a guest/host system as well as for a single component chiral nematic phase by ... 

Another example (which up to now seems very difficult to achieve) is based on chains dissolved in a cholesteric phase. This is a liquid where the molecules locally have one direction of alignment but where this direction has a helical twist in space. If we start with chains which are not optically active, crosslink them by an optically inactive agent, and then wash out the cholesteric solvent (replacing it by an achiral solvent), we should obtain a gel which has an optical rotatory power (a memory of its preparative state) although all its components do not distinguish right from left. ... 

First it was argued to be due to a chiral molecular configuration characteristic of the particular type of bent-shape molecules, such as twisted or propeller shape (conformational chirality). The concept of conformational chirality was supported by simulations by Earl et al. [61], and was demonstrated by the observation that doping calamitic cholesteric liquid crystal by achiral bent-core molecules can lead to a decrease of the helical pitch, indicating an enhanced rotatory power of the mixture [62]. Unfortunately there is no proof that the decrease of the pitch is not due to a decrease of the twist elastic constant caused by the addition of bent-core units. Although the conformational chirality is usually not questioned in the solid B4 phase [20], its role has been questioned by Walba et al. [20] by arguing that these chiral conformations have very short lifetime, therefore they average out in fluid smectic, such as SmCP or SmCo phases. 

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