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Chapter: Modern Analytical Chemistry: Spectroscopic Methods of Analysis

Spectroscopy Based on Scattering

1. Origin of Scattering 2. Turbidimetry and Nephelometry

Spectroscopy Based on Scattering

The blue color of the sky during the day and the red color of the sun at sunset result from the scattering of light by small particles of dust, molecules of water, and other gases in the atmosphere. The efficiency with which light is scattered depends on its wavelength. The sky is blue because violet and blue light are scattered to a greater extent than other, longer wavelengths of light. For the same reason, the sun appears to be red when observed at sunset because red light is less efficiently scattered and, therefore, transmitted to a greater extent than other wavelengths of light. The scat- tering of radiation has been studied since the late 1800s, with applications begin- ning soon thereafter. The earliest quantitative applications of scattering, which date from the early 1900s, used the elastic scattering of light to determine the concentra- tion of colloidal particles in a suspension.

Origin of Scattering

A focused, monochromatic beam of radiation of wavelength λ, passing through a medium containing particles whose largest dimensions are less than 3/2 λ is ob- served to scatter in all directions. For example, visible radiation of 500 nm is scat- tered by particles as large as 750 nm in the longest dimension. With larger parti- cles, radiation also may be reflected or refracted. Two general categories of scattering are recognized. In elastic scattering, radiation is absorbed by the analyte and re-emitted without a change in the radiation’s energy. When the radiation is re-emitted with a change in energy, the scattering is said to be inelastic. Only elas- tic scattering is considered in this text.

Elastic scattering is divided into two types: Rayleigh, or small-particle scatter- ing, and large-particle scattering. Rayleigh scattering occurs when the scattering particles largest dimension is less than 5% of the radiation’s wavelength. The inten- sity of the scattered radiation is symmetrically distributed (Figure 10.53a) and is proportional to its frequency to the fourth power (v4), accounting for the greater scattering of blue light compared with red light. For larger particles, the distribution of scattered light increases in the forward direction and decreases in the backward direction as the result of constructive and destructive interferences (Figure 10.53b).

Turbidimetry and Nephelometry

Turbidimetry and nephelometry are two related techniques in which an incident source of radiation is elastically scattered by a suspension of colloidal particles. In turbidimetry, the detector is placed in line with the radiation source, and the  decrease in the radiation’s transmitted power is measured. In nephelometry, scat- tered radiation is measured at an angle of 90° to the radiation source. The similarity of the measurement of turbidimetry to absorbance, and of nephelometry to fluores- cence, is evident in the block instrumental designs shown in Figure 10.54. In fact, turbidity can be measured using a UV/Vis spectrophotometer, such as a Spectronic- 20, whereas a spectrofluorometer is suitable for nephelometry.

Turbidimetry Versus Nephelometry 

Choosing between turbidimetry and neph- elometry is determined by two principal factors. The most important consideration is the intensity of the transmitted or scattered radiation relative to the intensity of radiation from the source. When the solution contains a small concentration of scattering particles, the intensity of the transmitted radiation, IT, will be very similar to the intensity of the radiation source, I0. As we learned earlier in the section on molecular absorption, determining a small difference between two intense signals is subject to a substantial uncertainty. Thus, nephelometry is a more appropriate choice for samples containing few scattering particles. On the other hand, tur- bidimetry is a better choice for samples containing a high concentration of scatter- ing particles.

The second consideration in choosing between turbidimetry and nephelometry is the size of the scattering particles. For nephelometry, the intensity of scattered ra- diation at 90° will be greatest if the particles are small enough that Rayleigh scatter- ing is in effect. For larger particles, as shown in Figure 10.37, scattering intensity is diminished at 90°. When using an ultraviolet or visible source of radiation, the opti- mum particle size is 0.1–1 μm. The size of the scattering particles is less important for turbidimetry, in which the signal is the relative decrease in transmitted radia- tion. In fact, turbidimetric measurements are still feasible even when the size of the scattering particles results in an increase in reflection and refraction (although a lin- ear relationship between the signal and the concentration of scattering particles may no longer hold).

Determining Concentration by Turbidimetry 

In turbidimetry the measured trans- mittance, T, is the ratio of the transmitted intensity of the source radiation, IT, to the intensity of source radiation transmitted by a blank, I0.

The relationship between transmittance and the concentration of the scattering par- ticles is similar to that given by Beer’s law

–logT = kbC                  ……………..10.36

where C is the concentration of the scattering particles in mass per unit volume (w/v), b is the pathlength, and k is a constant that depends on several factors, in- cluding the size and shape of the scattering particles and the wavelength of the source radiation. As with Beer’s law, equation 10.36 may show appreciable devia- tions from linearity. The exact relationship is established by a calibration curve pre- pared using a series of standards of known concentration.

Determining Concentration by Nephelometry 

In nephelometry, the relationship between the intensity of scattered radiation, IS, and the concentration (% w/v) of scattering particles is given as

IS = kSI0C                 ……………..10.37

where kS is an empirical constant for the system, and I0 is the intensity of the inci- dent source radiation. The value of kS is determined from a calibration curve pre- pared using a series of standards of known concentration.

Selecting a Wavelength for the Incident Radiation 

Selecting a wavelength for the incident radiation is based primarily on the need to minimize potential interfer- ences. For turbidimetry, where the incident radiation is transmitted through the sample, it is necessary to avoid radiation that is absorbed by the sample. Since ab- sorption is a common problem, the wavelength must be selected with some care, using a filter or monochromator for wavelength selection. For nephelometry, the absorption of incident radiation is not a problem unless it induces fluorescence from the sample. With a nonfluorescent sample there is no need for wavelength selection, and a source of white light may be used as the incident radiation. When using a filter or monochromator, other considerations include the dependence of scattering intensity, transducer sensitivity, and source intensity on the wavelength. For example, many common photon transducers are more sensitive to radiation at 400 nm than at 600 nm.

Preparing the Sample 

Although equations 10.36 and 10.37 relate scattering to the concentration of scattering particles, the intensity of scattered radiation is also in- fluenced strongly by the particle’s size and shape. For example, samples containing the same number of scattering particles may show significantly different values for –logT or Is depending on the average diameter of the particles. For a quantitative analysis, therefore, it is necessary to maintain a uniform distribution of particle sizes throughout the sample and between samples and standards.

Most turbidimetric and nephelometric methods rely on the formation of the scattering particles by precipitation. As we learned in the discussion of precipitation gravimetry , the properties of a precipitate are determined by the condi- tions used to effect the precipitation. To maintain a reproducible distribution of particle sizes between samples and standards, it is necessary to control parameters such as the concentration of reagents, order of adding reagents, pH, temperature, agitation or stirring rate, ionic strength, and time between the precipitate’s initial formation and the measurement of transmittance or scattering. In many cases a surface-active agent, such as glycerol, gelatin, or dextrin, is added to stabilize the precipitate in a colloidal state and to prevent the coagulation of the particles.


Turbidimetry and nephelometry are widely used to determine the clar- ity of water, beverages, and food products. For example, the turbidity of water is de- termined using nephelometry by comparing the sample’s scattering to that of a set of standards. The primary standard for measuring turbidity is formazin (Figure 10.55), which is an easily prepared, stable polymer suspension.26 Formazin prepared by mix- ing a 1 g/100 mL solution of hydrazine sulfate, N2H4•H2SO4, with a 10-g/100 mL solu- tion of hexamethylenetetramine produces a suspension that is defined as 4000 neph- elometric turbidity units (NTU). A set of standards with NTUs between 0 and 40 is prepared and used to construct a calibration curve. This method is readily adapted to the analysis of the clarity of orange juice, beer, and maple syrup.

A number of inorganic cations and anions can be determined by precipitating them under well-defined conditions and measuring the transmittance or scattering of radiation from the precipitated particles. The transmittance or scattering, as given by equation 10.36 or 10.37 is proportional to the concentration of the scatter- ing particles, which, in turn, is related by the stoichiometry of the precipitation re- action to the analyte’s concentration. Examples of analytes that have been deter- mined in this way are listed in Table 10.15. The turbidimetric determination of SO42– in water following its precipitation as BaSO is described in Method 10.5.


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