Basic Chemometric Techniques in Atomic Spectroscopy
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Further work by Ben-Gera and Norris consolidates the approach of using NIR spectroscopy and originated one of the most cited paper in the field. After the door had been opened and the potentialities demonstrated by the pioneers, NIR spectroscopy encountered fast development impelled mainly by instrumental spectrophotometer improvements associated with spectral data acquisition and their treatment micro-computer and which, to a great extent depended on the new discipline of Chemometrics, 18 which supplies the tools for gathering information and its wise use.
A recent review, has been published emphasising one of the main qualities of NIR spectroscopy: its rapid-response as an analytical tool. In Brazil, the first contributions to the field of applied analytical NIR spectroscopy can be traced back to Possibly, other pioneering uses of NIR in Brazil were carried out. However, these have not been reported in a traceable publication. The attribution of the year of for the first Brazilian contribution to NIR is in agreement with the contents of the preface of the first edition of the book by Williams and Norris on NIR technology where is it can be found that " For an analytical chemist trained in classical methodology, such as the author and many of his contemporary colleagues, perhaps one of the most significant and motivating examples is the replacement of a wet chemical procedure the Kjeldhal method for determination of protein in commodities wheat, corn and soybean, for example , by the direct NIR method.
The Kjeldhal method, as every analytical chemist well knows, is a quite robust and accurate method for determination of protein in a multitude of samples, mainly commodities. The method is based on the digestion of the ground grain in concentrated sulphuric acid containing a catalyst such as mercury or selenium.
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After an hour or so the digested product is made alkaline and submitted to a distillation. The distilled ammonia is collected in standard boric acid solution and, finally, the excess acid is titrated with standard sodium hydroxide solution. This cumbersome and time consuming procedure has been replaced by the NIR spectroscopic method which can directly determine the protein content of the whole or ground grain, through diffuse reflectance, in less than one minute, generating virtually no hazardous residue.
On the other hand, it is also wise, in order to be impartial, to alert the reader that, as marvellous it can appear at first glance, NIR technology is and will be always heavily dependent on the existence of good and acceptable reference methods as the Kjeldhal method. That is because at the learning stage modelling stage the direct method based on NIR needs to be able to identify the spectral characteristics or which combination of those characteristics are to be correlated for, in the above example, determining protein content in grain. The difference between failing or succeeding in this task is greatly dependent on the quality of the reference values associated with the samples in the training set.
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Nevertheless, once the learning stage is concluded, the final result is perhaps the closest that our present technology is able to produce of an ideal analytical method. In order to access the origin of a NIR spectra, to be able to interpret it and have an important tool to guide in analytical method development, one should be familiar with the fundamentals of vibrational spectroscopy. The NIR spectrum originates from radiation energy transferred to mechanical energy associated with the motion of atoms held together by chemical bonds in a molecule.
Although many would approach method development in a purely empirical way, knowledge of the theory can help to look at the important wavelengths and quicker optimisation of the modelling stage. Vibrational spectroscopy. At ambient temperature most of the molecules are in their fundamental vibrational energy levels. Atoms or group of atoms participating in chemical bonds are displacing one in relation to the other in a frequency that is defined by the strength of the bond and the mass of the individual bonded atoms or their groups.
The amplitudes of these vibrations are of a few nanometers and will increase if some energy is transferred to the molecule. This energy can be transferred from a photon of a given wavelength l , for which the energy E p can be given by:. The classical mechanical model for a diatomic molecule.
The simplest classical model employed to have a didactic insight on the interaction of radiation and matter in the NIR spectral region depicts a diatomic molecule as two spherical masses m 1 and m 2 connected with a spring with a given force constant k. The molecular vibration can be described by a simplified model supposing a harmonic oscillator for which the potential energy V , as a function of the displacement of the atoms x , is given by:.
Figure 1A shows the behaviour of the potential energy as a function of atom displacement from the equilibrium minimum energy position. This first approach is useful to understand the concept of vibrational energy. However, it fails when a microscopic system such as molecules is being considered.
The failure arises from the fact that molecular systems can not assume the continuous energy profile predicted by the classical "balls-on-spring" model. The molecular system can only have some discrete energy levels E u defined by quantum mechanics by the equation:. In the classical model this frequency is defined by:. Furthermore, for this model, the difference of energy between two adjacent states is always the same see Fig. The energy of the electromagnetic radiation that is absorbed in order to promote the molecule to an excited level should match the difference between two adjacent energetic levels.
Therefore, the photon energy must be. Figure 2 shows the effect of photon absorption on the energy and amplitude of vibration. The classical analogue to this behaviour is the concept of resonance. In this concept, the physical characteristics of a "string" stretched between two supporting points, such as its linear density and the force by which it is stretched, will define its natural frequency of vibration as a guitar string does.
The amplitude of this natural vibration therefore, its energy can be increased by exposing the string to an acoustic wave propagating in the air, with the same frequency, produced, for example, by a distant stroked string with the same characteristics. The first string undergoes no energy change if the acoustic wave frequencies and the natural frequency do not match each other.
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Similarly, only radiation of a certain frequency and wavelength can excite the vibrational levels of molecules. However, this model fails in the molecular world because it is not a quantum model. In the "string world" , the energy they can obtain from the exciting mechanical wave can increase continuously while a "quantum string" is able to vibrate at only a given frequency and at only some pre-defined amplitude. Although the harmonic model can help understanding vibrational spectroscopy, it produces some disappointing restrictions for NIR spectroscopy because it can not permit transitions where Du is greater than 1.
Also, the vibrations in the harmonic model are independent and their combinations would not exist under the restrictions imposed by the model. Nevertheless, both overtones and combination bands exist. The anharmonic model. Figure 1B shows a more realistic mechanical model for a diatomic molecule. The molecule is still approximated by two balls connected with a spring.
However, the model considers some non-ideal behaviours of the oscillator which account for repulsion between electronic clouds when the atomic nuclei approach notice how the potential energy rises fasten than in the harmonic model and a variable behaviour of the bond force when the atoms move apart from one another.
In fact, in a real molecule, the over displacement "strengthening of the spring" of the atomic nuclei will cause molecule bond rupture with consequent dissociation of the atoms. A complex function of the potential energy is assumed to describe the last effect which can be approximated by using higher order terms of displacement, as depicted in the equation.
A function that approximates the anharmonic behaviour of a diatomic molecule is the Morse function that describes the potential energy of the molecule using the equation:. Applying quantum mechanics to the Morse equation results in the vibrational levels being described by the equation:. These two types of bands are the most common absorption bands in the NIR spectral region. It also predicts that the separation between two adjacent energy levels decreases with u, the vibrational quantum number. Under the assumptions of the anharmonic model, the vibrations are no longer independent of each other and can interact with one another.
Therefore, the total vibrational energy E u contains cross-terms from more than one vibration in the molecule:.
Anharmonicity can also be present in the electrical properties of a molecule. Specifically, it affects its dipole moment which, in an anharmonic model, does not have a linear dependence with the interatomic distance. This kind of anharmonicity can provide the way for overtones and combination bands to occur even if no mechanical deviation of the harmonic model is observed for a given system.
Origin and intensity of a NIR absorption band. So far, it is possible to understand from theory that radiation of a given frequency, capable to supply exactly the energy between two vibrational levels or of their overtones or combinations of two or more vibrations, can be absorbed by the molecule and can produce excitation to a higher vibrational energy level. The match of radiation energy with the energy difference between two vibrational levels causes a selective response of the molecular system to the incident radiation.get link
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It means that in a given wavelength range, some frequencies will be absorbed, others that do not match any of the energy differences possible for that molecule will not be absorbed while some will be partially absorbed. This complex figure of the intensity of absorption versus wavelength constitutes the absorption spectra of a substance or sample. However, only the energy match between photons and vibrational levels is not sufficient for radiation absorption. For a vibration to be active, it is necessary that the electrical oscillating field of the electromagnetic wave light can interact with the molecule.
This can only occur if the displacement of the atoms in a vibrational mode can produce a change in the dipole moment of the molecule or in the local group of vibrating atoms. While this is true considering a fundamental mode, it is worth noting that, for combination bands permitted by anharmonicity, it would be necessary that only one of the combining vibrations be active causing dipole change.
This feature may cause some vibrations, which can not be observed in the middle infrared, to be displayed by a NIR spectrum. The intensity of a given absorption band is associated with the magnitude of the dipole change during the displacement of atoms in a vibration and with its degree of anharmonicity. Both phenomena are present in great intensity associated with bonds involving the hydrogen atom and some other heavier element such as carbon, nitrogen and sulphur.
Therefore, it allows to predict the overtones and combinations of the fundamental vibrations of such bonds to occur in the region of energy associated with NIR photons.
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Intensities are in between 10, for combinations, up to , for successive overtones, times lower than the absorption resulting from fundamental vibrations. The spectral occurrences in the NIR region are dominated by overtones and combination absorption bands. However, some other effects, associated with the higher order terms in equation 8, may be observed and contribute to the complexity of the NIR spectrum.
Coupling or resonance between different vibrations of the same functional group can occur as a function of the third and fourth order terms of equation 8. Fermi resonance occurs between a fundamental and an overtone when their difference in energy is very low. This type of resonance results in a greater separation between the position of the two bands and in the intensification of the overtone band.
Darling-Dennison resonance may promote the interaction between two high level overtones of a molecule and a combination band, for example, and is particularly intense for bonds containing hydrogen atoms. The complexity of the combination spectral region in the NIR spectrum of hydrocarbons is partly due the possibility of resonance between the combination bands and high order overtone for C-H bonds.
Additional information on the theory regarding vibrational NIR spectroscopy is found in more detail in several references.