Refractive index, relationship

The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. 

The numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently... 

Both a film and c film can be further divided into positive or negative films depending on the relative values of the extraordinary refractive index tie and the ordinary refractive index Table 8.1 lists aU the types of compensation films and their refractive index relationship. In our analyses, we focus on the uniaxial films. As a general rale, a positive uniaxial film means Tie > no, otherwise, rig < tig for a negative uniaxial film. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

ICUMSA (1) has adopted tables showing the relationship between the concentration of aqueous solutions of pure sucrose, glucose, fmctose, and invert sugar and refractive index at 20.0°C and 589 nm. 

Equations have been developed that determine the relationship of the refractive index of sucrose solutions between 0—85% concentration, 18—40°C, and 546—589 nm. 

Water Content and Refractive Index. The water content of a hydrophilic contact lens is a determinant of other properties. The relationship of water content and Dk is discussed above. Water content in lenses is inversely related to refractive index (23), a key property for vision correction. A lens material with a higher refractive index refracts light to a greater degree, allowing more vision correction with a thinner material. The water content of a lens is generally determined gravimetricaHy or inferred from the relationship to refractive index, measured with a refractometer (24). 

It is important to note that comparable information to that obtained from infra-red spectroscopy can in principle be obtained from refractive index measurements. It has been shown that for a transversely isotropic film, the relationship equivalent to 11(c) is... 

Using the ideal gas law and the relationship (n — 1) oc p between refractive index n and density p leads us to the refractive index structure function. 

By deriving or computing the Maxwell equation in the frame of a cylindrical geometry, it is possible to determine the modal structure for any refractive index shape. In this paragraph we are going to give a more intuitive model to determine the number of modes to be propagated. The refractive index profile allows to determine w and the numerical aperture NA = sin (3), as dehned in equation 2. The near held (hber output) and far field (diffracted beam) are related by a Fourier transform relationship Far field = TF(Near field). 

The polarisability, a, of the molecule is proportional to the refractive index increment dn/dc, and to the relative molar mass of the molecule in question. The full relationship is ... 

Published refractive index data for the mobile phase, polystyrene, polyacrylonitrile, and the two monomers were used to calculate refractive index detector calibrations for the two homopolymers. The published data were used to determine relationship between refractive index increments of monomer and corresponding homopolymer. Chromatographic refractometer calibrations for the two homopelymers were then calculated from experimentally measured calibration data for the two monomers. 

We now focus our attention on the presence of the unperturbed donor quantum yield, Qd, in the definition of R60 [Eq. (12.1)]. We have pointed out previously [1, 2] that xd appears both in the numerator and denominator of kt and, therefore, cancels out. In fact, xo is absent from the more fundamental expression representing the essence of the Forster relationship, namely the ratio of the rate of energy transfer, kt, to the radiative rate constant, kf [Eq. (12.3)]. Thus, this quantity can be expressed in the form of a simplified Forster constant we denote as rc. We propose that ro is better suited to FRET measurements based on acceptor ( donor) properties in that it avoids the arbitrary introduction into the definition of Ra of a quantity (i />) that can vary from one position to another in an unknown and indeterminate manner (for example due to changes in refractive index, [3]), and thereby bypasses the requirement for an estimation of E [Eq. (12.1)]. 

When chloroform was added, the equilibrium response of the sensor progressively decreased. This is probably related to the combination of the nonlinear behavior of the effective refractive index of the coupled cladding mode on the overlay refractive index with the nonlinear relationship between adsorbed mass of... 

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

The relationship between the refractive index and the amount of dry substance content is well known for sucrose and is the basis for the degree Brix (°Brix) scale. It is arbitrarily set such that 1° Brix is equal to a concentration of 1% sucrose. In other words, the °Brix scale indicates the number of grams of sucrose per 100 g of solution. This relationship also holds for a large number of similar substances and finds extensive use in the food industry. For example, a reading of 40° Brix would mean that the sample contained 40 g of solid per 100 g of solution. 

---