Refractive index derivation

The net effect of inserting the complex refractive index, derived from the damped oscillation of the electrons, is that the plane wave traveling through a material with refractive index n — ik undergoes attenuation as shown in Figure 9.10. Hence the material is... 

Compound Boiling point (°C) Refractive index Derivative Melting point (°C) Ref. 

Some of the earliest chemical studies of nonhydrocarbons, which resulted in the isolation of numerous strong acids and bases, were conducted at the University of Texas under the leadership of Lochte and Littman (I). This work used the classical extraction of petroleum with mineral acids and caustic followed by chemical identification (boiling point, refractive index, derivatives, etc.). Since only strong Bronsted acids and bases can be isolated by aqueous solvents, their identifications were limited to low-molecular-weight species aqueous solvents also do not isolate weak acids or bases (low pK values). 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

Because of the chemical inertness of the paraffin hydrocarbons and of the closely related cycZoparaffins, no satisfactory crystalline derivatives can be prepared. Reliance is therefore placed upon the physical properties (boding point, density, and refractive index) of the redistilled samples. These are collected together in Table III,6. 

Chakactkrisation of Unsaturatkd Aliphatic Hydrocarbons Unlike the saturated hydrocarbons, unsaturated aliphatic hydrocarbons are soluble in concentrated sulphuric acid and exhibit characteristic reactions with dUute potassium permanganate solution and with bromine. Nevertheless, no satisfactory derivatives have yet been developed for these hydrocarbons, and their characterisation must therefore be based upon a determination of their physical properties (boiling point, density and refractive index). The physical properties of a number of selected unsaturated hydrocarbons are collected in Table 111,11. 

Di- and poly-halogenated aliphatic hydrocarbons. No general procedure can be given for the preparation of derivatives of these compounds. Reliance must be placed upon their physical properties (b.p., density and refractive index) and upon any chemical reactions which they undergo. 

The low reactivity of aliphatic ethers renders the problem of the preparation of suitable crystalline derivatives a somewhat difficult one. Increased importance is therefore attached to the physical properties (boding point, density and refractive index) as a means for providing preliminary information. There are, however, two reactions based upon the cleavage of the ethers which are useful for characterisation. 

Location of the compound within a class (or homologous series) of compounds. Reference to the literature or to tables of the physical properties of the class (or classes) of organic compounds to which the substance has been assigned, will generally locate a number of compounds which boil or melt within 6° of the value observed for the unknown. If other physical properties e.g., refractive index and density for a hquid) are available, these will assist in deciding whether the unknown is identical with one of the known compounds. In general, however, it is more convenient in practice to prepare one, but preferably two, crystalhne derivatives of the substance. 

The refractive index of a liquid is recorded as where t is the temperature at which the measurement is made, and D refers to the wave length of the D line of sodium. As already pointed out, it is usual to determine both the refractive index and the density of the liquid at 20° in any case they should be determined at the same temperatme. These two constants are useful in assisting the characterisation of a pure hquid they are particularly valuable for ahphatic hydrocarbons and similar compounds where the methods of characterisation by the formation of solid derivatives are not entirely satisfactory. 

Capillary gc/ms, hplc, nmr, ir, and uv are all analytical methods used by the terpene chemist with a good Hbrary of reference spectra, capillary gc/ms is probably the most important method used in dealing with the more volatile terpenes used in the davor and fragrance industry (see Flavors and spices). The physical properties of density, refractive index, boiling point, melting point of derivatives, and specific rotation are used less frequendy but are important in defining product specifications. 

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

Br. CHa. CHa. CHa. CH(NHa). CH(CHa). CHa. CHjBr HBr. which on treatment with dilute alkali gives di-heliotridane (II). As the latter contains two asymmetric carbon atoms, two diastereoisomeric racemates might be produced in this reaction but only one was formed. It had density and refractive index in general agreement with those recorded for Z-heliotridane, as were also the melting points of characteristic derivatives. Density Df °0-902, refractive index wf, 1-4638 (<. with Adams and Rogers,3i Df ° 0-935, iijf° 1-4641), picrate, m.p. 234-6° (literature 232-6°), picrolonate, m.p. 162-3°, aurichloride, m.p. 200-1° (Konovalova and Orekhov give for these two constants 152-3° and 199-200° respectively). 

Some diamines carrying very bulky substituents like cardo groups can give colorless polyimides. For example, the bis-9,9-(4-aminophenyl)fluorene (FDA) or brominated and acetylenic FDA derivatives react with 6FDA giving copolymer films62 with low birefringence (low difference between in-plane and out-of-plane refraction index) (Fig. 5.8). A new cardo diamine l,l-bis[4-(4-aminophenoxy)phenyl]cyclododecane (Fig. 5.8) reacts with different aromatic dianhydrides with formation of colorless polyimides.63... 

Detection of the these types of compounds are sometimes difficult as many components of cosmetic products are aliphatic, do not possess a UV chromophore and are not easily reacted to give fluorescent derivatives. Providing the concentration of the component of interest is sufficiently high, then a refractive index detector is often used. If... 

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). 

Adsorption chromatography using small particle silica or alumina has also been employed in the separation of biologically meaningful substances. Phospholipids, for example, have been separated on silica (38). One of the big problems for such substances is detection, since many of the compounds are not U.V. active. Generally, the refractive index detector is employed for isocratic operation, and the moving wire detector for gradient operation. Formation of U.V.-active derivatives is also possible (39). 

Ellipsometry is used to study film growth on electrode surfaces. It is possible to study films at the partial monolayer level and all the way up to coverage of thicknesses of thousands of angstroms while doing electrochemical measnrements. To get nseful data it is important to determine A and j/ for the bare electrode snrface and the surface with a film. These data are processed to derive the film thickness, d, and the refractive index, h, which consists of a real (n) and imaginary part (k), h = n- ik. So ellipsometry gives information on the thickness and refractive index of snrface hlms. 

---