Molar refraction definition

The electromagnetic wave theory of light enables the definition of the molar refractivity... 

Hence, several definitions of the molar refraction have been proposed in the literature, correlating the refractive index with the chemical structure of electrically insulating materials. Resuming ... 

Alternative definitions of molar refractivity were proposed by Gladstone and Dale (MRgd) [Gladstone and Dale, 1858] and by Vogel (MRy) [Vogel, 1948] as ... 

R2 = MRa - MR = MRa - (2.83195 Vx - 0.52553) where MRa is the molar refractivity of the considered compound and MR the molar refractivity of the n-alkane with the same characteristic volume Vx. The parameter R2 can be considered a polarizability descriptor and is called excess molar refractivity. By definition, / 2 = 0 for all n-alkanes, and the same holds for branched alkanes. 

By the definition given above, molecular descriptors are divided into two main classes -+ experimental measurements, such as - logP, - molar refractivity, - dipole moment, -> polarizability, and theoretical molecular descriptors, which are derived from a symbolic representation of the molecule and can be further classified according to the different types of molecular representation. 

A consensus definition of a drug-like molecule has been derived from the analysis of the CMC database by defining qualifying (covering 80% of drug molecules) ranges of calculated physical properties such as molecular weight, log P, molar refractivity, and number of atoms ... 

The refractive index is usually estimated in terms the molar refraction R, which quantifies the intrinsic refractive power of the structural units of the material. Several definitions have been proposed for R. Two of these definitions incorporate both of the key physical factors determining the refractive index, and are thus especially useful. Equation 8.5 expresses n in terms of the molar refraction RT T according to Lorentz and Lorenz [1,2], and Equation 8.6 expresses n in terms of the molar refraction Rgd according to Gladstone and Dale [3]. 

On the other hand, in aromatic compounds, particularly in benzene, a decrease is apparent in the molar refraction. This depression is specific to the aromatic character and is consistent with the fact that, on account of the ring arrangement of the three double bonds within the nuclear framework, a definite distribution of negative charge density occurs. The same consequence was deduced from quantum-mechanical considerations by the far-reaching studies of Hiickel, Pauling and Slater. It... 

An alternative to improving atomic/ionic refractions was to express molecular refraction through bond increments. A system of bond refractions is definitely superior to the system of atomic refractions, as it allows to account for chemical interactions explicitly. The concept of bond refraction was introduced by Bachinskii [183] who suggested that the molar refraction (as well as volumes, heats of combustion, etc) of organic compounds can be calculated of bond increments. According to Bachinskii, Rc-c =l/4f c + l/4 c. = l/47Jc + etc. This method is not quite con-... 

According to another definition, by Gladstone, molar refraction Rgd is given by... 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

More than 30 years ago, Scott, Obenhaus, and Wilson (135) suggested that for lithium chloride, a solute to solvent ratio of 1 10 corresponded to a definite composition, and they quoted earlier measurements (134) as indicating two distinct, definite values for the magnetic susceptibility of lithium chloride above and below the concentration, corresponding to a decahydrate in solution. Likewise, anomalies were also found in the density of such solutions. Scott, Obenhaus, and Wilson also quoted Hiittig and Keller (83) who found that the densities, refractive indices, and coefficient of extinction of lithium halide solutions showed discontinuous changes with concentration for molar ratios of water to solute of 6, 30, and 75. 

This behavior occurs until a certain high temperature is reached denoted and called the critical temperature. At that temperature, the constant pressure plateau shrinks into a single point (point C) called the critical point The molar volume at that point is called critical molar volume and the pressure is the critical pressure P. A gas cannot be condensed to a liquid at temperatures above and there is no clear distinction between the liquid and gaseous phases because the two states cannot coexist with a sharp boundary between them. Experimentally, if a certain amount of gas and liquid is placed inside a pressurized container with transparent quartz windows and kept below T, two layers will be observed, separated by a sharp boundary. As the tube is warmed, the boundary becomes less distinct because the densities, and therefore the refractive indices, of the liquid and gas approach a common value. When the T is reached, the boundary becomes invisible and the iridescent aspect exhibited by the fluid is called critical opalescence. Hence the following definitions can be drawn for the critical constants of a real gas. 

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