## 1. Introduction

The interest in the separation of enantiomers of organic compounds has been recently increased in the food, medicine and cosmetic industries. As it is well know, the chirality is extremely important for living systems, because most of the biomolecules are chiral ones* .* For example, glucose, a sugar exists in one conformation; while the opposite enantiomer cannot be used as a food source. Biochemistry uses only one hand and not the other however the reason for this has not been understood, so far. Over half of the organic compounds in drugs are chiral whose different enantiomers have different effects. For instance, Ritalin prevents hyperactivity in children in one enantiomer, whereas it has not effect when the opposite enantiomer is used. Another example is thalidomide: one enantiomer of thailomide can cure morning sickness of pregnant women, whereas the other causes birth defects. The sense of smell is also sensitive to the chirality of the odor molecules. For instance, limonene has an orange smell whereas the opposite enantiomer smells like lemon [1].This exemplifies the fact that separation of molecules by chirality is an important process in biochemistry and in the pharmaceutical industry. In this paper we suggest a method to optically monitoring the chiral sorting of molecules performed by an elastomer liquid crystal.

Liquid crystal elastomers combine the rubbery elastic properties with the liquid crystals (LC) anisotropy [2]. When these stiff molecules are joined to a large and flexible polymer chain, they leave their muddy liquid macroscopic form and acquire the appearance of a rubbery network. Particularly, imprinted cholesteric elastomers acquire its chirality from an induced chiral structure instead of chiral molecules. Upon cross-linking nematic polymers in a chiral solvent to form a gel, the solvent, which causes a natural twist to the nematic is thus removed but nonetheless leaves behind an imprinted cholesteric elastomer [3]. A spectacular property of imprinted networks is their capacity to preferentially absorb and retain right or left molecules from a racemic solvent which renders them chiral pumps. Moreover the elastomersare photonic materialsin the sense that exhibit an optical band structure just as the one shown by electrons in metals and semiconductors. Elastomers provide a large spectrum of applications that exploit the possibility of externally handle a band structure by various types of agents like mechanical stress, electric fields chemical solvents for designing devices such as optical sensors, mirrors, laser and filters [2] [4].

The purpose of this chapter is to propose an optical method to determine the volume fraction of preferentially absorbed molecules by measuring the transmittance and reflectance spectra during a preferentially absorbing process. Specifically, we are interested in calculate the reflectance and transmittance of circularly polarized light for oblique incidence due to a cholesteric elastomer, assuming arbitrary values of chiral order parameter,

## 2. Elastic formulation

A cholesteric elastomer has locally a nematic structure. Consequently, the director vector

The chiral order parameter

The energy for an elastomer formed under thepresence of a chiral solvent which is subsequently replaced with an achiral one is given by [8],

The Frank free energy to twist the material is given by

associated with the first term of the eq. (1)- tend to unwind the cholesteric helix but it finds resistance to rotate in the anchoring of the rubbery network- associate with the second term of eq. (1).

There are two forms of modifying this relation, i) by increasing the nematic penetration depth which amounts to have a weaker gel or one with smaller anisotropy, ii) by enlarging the Frank free energy. The chiral imprinting will be lost if

Eq. (1) can be expressed in terms of chiral parameter order as,

The equilibrium configuration can be obtained by minimizing

which in this case turns out to be

Notice that if

which is the simple pendulum equation. Hence, for large values of

where

## 3. Optical description

As any chiral material whose axis of chiral nonhomogeneity is along the

where

Maxwell curl equations (in MKS units) for media whose dielectric tensor is only

where

where

In this equation, the

with

Equation (12) can be solved by a variety of techniques. We chose to implement the piecewise homogeneity approximation method. The final result is the computation of a transfer matrix

## 4. Boundary value problem

Suppose that plane waves are obliquely incident on a cholesteric of finite thickness from both half-spaces

where

Continuity of the tangential components of the electric and the magnetic fields across the planes

where the matrix

By virtue of Eqs. (16), (17) and (19), we obtain the matrix algebraic equation

where the so called transfer matrix is given by

and the symbol

The result of solving Eq. (21) is best arranged as

where

where

In what follows we shall restrict our calculation to the case in which the incident waves are coming only from the left hand side that is we take

## 5. Spectra

In our calculations we have chosen the physical amounts of a real cholesteric elastomer material

Fig. 7 presents the corresponding trasmittances to Fig.6. The case without solvent (

In the Fig. 9 is shown the reflectance of left and right circularly polarized light as a function of wavelenght and the chiral order parameter to oblique incidence. Complementary, In the Fig. 10 is shown the same of the Fig.9 as function of wavelenght and the parameter

## 6. Conclusions

We have obtained the circularly polarized reflectances and transmittances as function of the chiral order parameter of a cholesteric elastomer immersed in a racemic solvent. We have found considerably changes in the bandwidth of the reflectance for left- and right-copolarized light under the presence of the solvent which are susceptible to be detected experimentally. We have obtained a

The modifications of the transmittance and reflectance spectra during a preferentially absorbing process suggest to utilize the optical spectra as an indirect method to determine the concentration of preferentially absorbed molecules during a segregation process.

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