Chirality and symmetry

The word chirality originates from Greek (hand). Chiral objects (and 

Chiral molecules, only left or only right, form chiral phases, left and right chiral molecules in equal amount form achiral (enantiomorphic) phases [6]. Consider a chiral molecule of a popular compound DOBAMBC (D(or L)-p-decyloxybenzyli-dene-p -amino-2methylbutyl cinnamate). It has an asymmetric carbon in its tail and form a chiral SmC phase in the range of 95-117°C, Fig. 3.5a. A molecule with a chiral tail looks like an ice-hockey stick and forms a helical liquid crystal phase. Feft and right forms of a chiral tail result in the left and right handedness of a molecule Fig. 3.6. On the other hand, chirality of cholesterol esters is exclusively due to a curvature of the molecular skeleton Fig. 3.5b. 

The synthesis of chiral molecules is a real challenge. There are, at least, three different approaches. 

In this section we will learn how to determine whether a compound is chiral or achiral. It is true that any compound with a single chirality center must be chiral. But the same statement is not necessarily true for compounds with two chirality centers. Consider the cis and tram isomers of 

Each of these compounds has two chirality centers, but the tram isomer is chiral, while the cis isomer is not chiral. To understand why, we must explore the relationship between symmetry and chirality. Let s quickly review the different types of symmetry. 

Broadly speaking, there are only two types of symmetry rotational symmetry and reflectional symmetry. The first compound above (the tram isomer) exhibits rotational symmetry. To visualize this, imagine that the cyclohexane ring is pierced with an imaginary stick. Then, while your eyes are closed, the stick is rotated  

This operation generated the same exact image 

after opening your eyes, it is impossible to determine whether or not the rotation occurred, then the molecule possesses rotational symmetry. The imaginary stick is called an axis of symmetry. Now let s consider the structure of the cis isomer  

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In Chapter 4, on molecular symmetry, 1 have added two new sections. One of these concerns the relationship between symmetry and chirality, which is of great importance in synthetic organic chemistry. The other relates to the connection between the symmetry of a molecule and whether it has a permanent dipole moment. 

Mead, C. A. Permutation Group Symmetry and Chirality in Molecules. 49, 1-86 (1974). 

Volume 49 C.A. Mead Symmetry and Chirality 23 figures. IV, 88 pages. 1974... 

Besides molecular shapes and amphiphilicity, chirality also has a large influence on LC self assembly, leading to series of LC phases with helical superstructures, reduced symmetry, and chirality induced frustration [43-46]. 

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