Absorbance, Lambert/Beer laws, color

Frequently, color strength is determined by the simpler and more easily reproducible measurement of the extinction of the dye solution. However, in many cases this does not agree with the values determined by dyeing because dyes in solution may not follow the Lambert-Beer law and are not always absorbed quantitatively by the fiber [25],... 

There are two fundamental laws to consider when we discuss absorption Beer s law and Lambert s law. Lambert s law states that equal thickness of materials cause equal amounts of absorption. Beer s law states that equal amounts of absorbing material cause equal absorption. Figure 2.5 illustrates these laws (Billmeyer and Saltzman, 1981). Both laws will only work in the absence of scattering and are not applicable in opaque or translucent materials. They are very useful in transparent materials, where the scattering due to the colorants and the polymers themselves (low refractive indices) is very low. 

The Lambert and Beer theory is reserved for transmittance calculations for very transparent samples. Dating back to the eighteenth and nineteenth centuries, the Lambert and Beer laws state that the absorbence [log(l/T)] for a transparent sample is proportional to the thickness and the concentration of the colorant [4]. 

Colorant Mixing. A colorant, whether a dye dissolved in a medium or pigment particles dispersed in it, produces color by absorbing and/or scattering part of the transmitted light. If only absorption is present, the Beer-Lambert law appHes ... 

As is known from the Beer-Lambert law, the absorbance A of a solution is the product of the absorption coefficient e, the optical path length of the solution Z, and the concentration of the colored species c, that is,... 

The simple visible spectrophotometer has been an important instrument in trace environmental analysis for many years. Colorless environmental contaminants must be chemically converted to a species which appears colored to the eye. The colored species will then exhibit regions of the visible electromagnetic spectrum where it will absorb photons. This absorption can be related to the Beer-Lambert or Beer-Bouguer Law of Spectrophotometry according to ... 

The experimental rate law can be determined by monitoring the concentration of one of the reactants or products as a function of time using spectroscopic means. For instance, the Beer-Lambert law states that the absorbance of a colored compound is directly proportional to its concentration (for optically dilute solutions anyway), so that the absorbance can be measured as the course of the reaction proceeds. The data are then fit to a model, such as the function that results when integrating one of the differential rate law equations. The integrated rate laws for some commonly occurring kinetics are listed in Table 17.1. Half-life equations are also included for some of the reactions in this table, where the half-life ftyi) is defined as the length of time that it takes for half of the initial reactant concentration to disappear. 

When the path length and colorant are kept constant, the Beer-Lambert law suggests a linear relationship between the absorbance and dye concentration at a given wavelength. Using Eq. 8.1 ... 

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