Optical Modeling Methods

For many liquid crystal devices, their optical properties cannot be calculated analytically because their refractive indices vary in space. In this chapter we will discuss methods which can be used to numerically calculate the optical properties of liquid crystal devices. 

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All methods mentioned in Table 1 operate (typically) in the frequency domain a monochromatic optical wave is usually considered. Two basically different groups of modeling methods are currently used methods operating in the time domain, and those operating in the spectral domain. The transition between these two domains is generally mediated by the Fourier transform. The time-domain methods became very popular within last years because of their inherent simplicity and generality and due to vast increase in both the processor speed and the memory size of modem computers. The same computer code can be often used to solve many problems with rather... 

High cell densities are not only a prerequisite for high productivity additionally an effective on-line control and modeling of the bioprocesses is necessary. For industrial applications, optical measurement methods are more attractive because they are non-invasive and more robust. The potential of the BioView sensor for on-line bioprocess monitoring and control was tested. For high-cell-density cultivation of Escherichia coli, maintaining aerobic conditions and removal of inhibitory by-products are essential. Acetic acid is known to be one of the critical metabolites. Information about changes in the cell metabolism and the time of important process operations is accessible on-line for optimization... 

This chapter deals with silyl-substituted carbocations. In Section II results of quantum chemical ab initio calculations of energies and structures of silyl-substituted carbocations are summarized1. Throughout the whole chapter results of ab initio calculations which relate directly to the experimental observation of silyl-substituted carbocations and their reactions are reviewed. Section m reports on gas phase studies and Section IV on solvolytic investigations of reactions which involve silyl-substituted carbocation intermediates and transition states. Section V summarizes the structure elucidation studies on stable silyl-substituted carbocations. It includes ultra-fast optical spectroscopic methods for the detection of transient intermediates in solution, NMR spectroscopic investigations of silyl-substituted carbocations in superacids and non-nucleophilic solvents, concomitant computational studies of model cation and X-ray crystallography of some silyl-substituted carbocations which can be prepared as crystals of salts. 

Beyond the simple thin surfactant monolayer, the reflectivity can be interpreted in terms of the internal structure of the layer, and can be used to determine thicker layers and more complex surface structures, and this can be done in two different ways. The first of these uses the optical matrix method [18, 19] developed for thin optical films, and relies on a model of the surface structure being described by a series or stack of thin layers. This assumes that in optical terms, an application of Maxwell s equations and the relationship between the electric vectors in successive layer leads to a characteristic matrix per layer, such that... 

It was also possible to analyze data from the DPPC/OA monolayers using the optical matrix method. A one-layer model represents an oversimplification of the complex structure of this monolayer, and the quality of the fits to experimental data is generally poorer than for the DPPC monolayer. Despite these problems it has been possible to estimate the relative volume fraction of DPPC, OA, and water in these mixed monolayers. It is apparent at all surface coverages that the volume fraction of DPPC is approximately twice that of OA, as expected, and that the volume fraction of water in the monolayer increased steadily as the monolayer was expanded to 70 A /molecule. 

Boxman et. al. suggest that more information can be obtained if the fluctuations in the signals from each detector are examined together with the mean values [150]. They note that this approach can identify whether the inaccuracy is due to insufficient sampling of the detector array or imperfections in the optical model. More recently Knight et. al. [151] developed an analytical inversion method that gave improved resolution and accuracy in size distribution measurement. 

The combination of plasmonics calculations to model the enhancing particles, and rigorous molecular treatment allow for a comprehensive model. The quantum optic model of Kali and co-workers [JO, 44] gives a unified treatment of a model molecule with two electronic states, and an arbitrary number of vibrational levels. Although more complete methods are possible, by adding different vibrational bands, for example, this includes the most important elements, and allows coupling to calculated plasmonic results. 

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