13.2.1 Electromagnetic Radiation

Infra‐red and Raman spectroscopies are often collectively referred to as vibrational spectroscopy, which is a study of the interactions between light and molecules where the interaction results in a change in the molecular vibrational energy state and the characteristics of light, such as intensity (I), wavelength (λ), propagation direction and polarisation. Light in the ultraviolet (UV), visible and infra‐red ranges are the parts of the spectrum of electromagnetic radiation that are used in this technique. Electromagnetic radiation can be represented by the classical wave model or the particle model. The classical wave model describes the electromagnetic radiation as an oscillating electric and magnetic field that propagate through space at the speed of light (∼3 × 10⁸ m/s in vacuum). The classical wave model has helped scientists to understand some of the properties of electromagnetic radiation such as diffraction and refraction. However, the classical wave model does not explain the particle behaviour of electromagnetic radiations such as the photoelectric effect. Albert Einstein had shown that there is a minimum frequency of radiation that is required for the ejection of electrons from metals when light is shone on the metal surface, and that it is independent of the radiation intensity. His observation can be explained by the particle model, where electromagnetic radiations are considered as particles called photons. Each photon contains a discrete amount of energy depending on the wavelength of the radiation, given by

13.1a

or

13.1b

or

13.1c

The symbol h is the Planck constant, which has a value of 6.626 × 10⁻³⁴ J s, and that wavenumber, ω, and frequency, ν, are related to wavelength, λ, by

13.2a

13.2b

Note that the electromagnetic radiation of a specific wavelength carries a specific amount of energy and therefore energy is said to be quantised. The concept of quantisation of energy is important in many spectroscopic studies because, in analogy to the photoelectric effect, a molecule can only be excited to a higher electronic or vibrational energy state when the incident light carries enough energy. UV–visible absorption spectroscopy and fluorescent spectroscopy are concerned with the electronic energy state transitions while infra‐red and Raman spectroscopies are concerned with the vibrational energy state transitions. The latter two spectroscopic methods produce spectra that are highly characteristic of the molecule.

13.2.2 Molecular Vibration

Atoms in a molecule are constantly oscillating even when they are in the non‐excited ground state. The periodic movement of atoms in a vibrating molecule generates an oscillating local electric field in the molecule. These periodic fluctuations in the electric field enable the molecule to interact with light because light waves (or photons) are also oscillating electric fields. The frequency, ν, of molecular vibrations can be estimated using the simple harmonic oscillation model

13.3

From Eq. (13.3), where m is the reduced mass of the atoms involved in the covalent bond and k is the strength of the bond, we can see that a smaller mass of the system and a stronger chemical bond will result in a higher vibrational frequency. For example, stretching vibrations that involve hydrogen atoms are often found in the high frequency (or wavenumber) region of the spectrum because of the low atomic mass of hydrogen atom. C–H, N–H and O–H (‘X’–H) stretching modes are found in the range of 2800–3800 cm⁻¹. Bands due to vibrations of single bonds (weaker), with the exception of X–H stretching modes, are often found below 1400 cm⁻¹ while bands due to the stretching vibrations of double and triple bonds (stronger) are found in 1400–1800 and 2000–2400 cm⁻¹ ranges, respectively. It is clear that the nature of the chemical bonding will determine the vibrational frequencies of the molecule. A list of vibrational frequencies of common function groups are listed in Table 13.1.

13.2.3 Vibrational Energy

The energy required for vibrational energy transitions to occur can be schematically presented on an energy diagram as shown in Figure 13.1. Once the frequency of the molecular vibration is known, Eqs. (13.1a) to (13.3c) can be used to calculate the energy band gap (ΔE) between the excited and the ground vibrational states. One of the conditions for a molecule to absorb light is when the energy of the light matches the energy band gaps. Figure 13.1 schematically illustrates that the energy band gap for electronic transitions is much greater than vibrational transitions. For electronic transitions to occur, lights with wavelengths in the ultraviolet or visible range are required. However, the energy of light that is required to excite molecular vibration falls within the mid‐IR range, which is between 2.5 and 40 μm (4000 and 250 cm⁻¹). The study of energy transitions within this wavelength range is therefore called vibrational spectroscopy, including infra‐red (mid‐infra‐red) and Raman spectroscopies. Infra‐red spectroscopy is the study of the absorption of infra‐red light by the sample, which results in excitations between vibrational energy levels. Raman spectroscopy, on the other hand, is a study of the inelastic scattering of light, which results in a change in the vibrational energy level of the molecule through a temporal virtual energy state (Figure 13.1).

13.2.4 Modes of Vibration

A chemical bond can vibrate through a stretching and/or bending motion. Among others, there are two most important types of stretching mode (symmetric and asymmetric) and four types of bending mode (scissoring, rocking, wagging and twisting) depending on the structure of the molecule. For the same functional group, stretching modes of vibration usually have higher energy (higher frequency/wavenumber) than bending modes of vibration. For example, the symmetric and asymmetric ν(CH₂) stretching modes of vibration are found in the 2800–3000 cm⁻¹ region while the δ(CH₂) bending modes of vibration are found around ∼1400 cm⁻¹. Note that stretching and bending modes of vibration are denoted by the symbols ν and δ, respectively. Examples of the various stretching and bending modes of vibration are illustrated in Figure 13.2.

13.2.5 Number of Vibrations

The total number of vibrations found in a molecule can be calculated by Eqs. (13.4a) and (13.4b) with

13.4a

for a linear molecule and

13.4b

for a non‐linear molecule, where N is the number of atoms in the molecule. Diatomic molecules such as hydrogen, oxygen and nitrogen (H₂, O₂ and N₂) are linear molecules and therefore have just one vibration. Water (H₂O) is a non‐linear molecule with three atoms and therefore has three modes of vibration (the symmetrical and asymmetrical stretching modes and a bending mode). In contrast, a small drug molecule such as ibuprofen (C₁₃H₁₈O₂) has 33 atoms, is a non‐linear molecule, and will have 291 vibrations. It can be seen that with just a relatively small number of atoms, a small molecule can produce a large number of distinct vibrations, resulting in a unique set of vibrational energy band gaps. The vibrational spectrum of a molecule is often distinctive, which is the basis of the high chemical specificity offered by these vibrational spectroscopic techniques. However, not all vibrations will produce a spectral band because of the different selection rules, which we will discuss below.

13.2.6 Infra‐red Spectroscopy

Infra‐red spectroscopy is a study of the absorbance (or transmittance) of infra‐red light through the sample. As a result of the absorption of infra‐red light, the vibrational energy state rises from the ground state to the first excited state, as shown in Figure 13.1. Molecules can only absorb light that has the same frequencies as their molecular vibrations. This is one of the conditions for light absorption. The second condition is that the molecular vibration must produce a change in dipole moment so that the periodic fluctuation of the electric field generated from the vibrating molecule can interact with the light. These two conditions are the selection rules for infra‐red absorption. Based on this principle, we can predict the types of covalent bond that will or will not produce infra‐red bands. For example, diatomic molecules (e.g. H₂, O₂ and N₂) have no change in dipole moment from their vibrations and therefore they do not absorb infra‐red light. These vibrations are considered as infra‐red inactive. Covalent bonds with permanent dipoles that produce a larger change in dipole moment during molecular vibration will produce stronger infra‐red absorption bands. For example, the carbonyl, C–O and N–O stretching modes of vibration can produce strong infra‐red absorption bands with larger molar absorptivities (also referred to as the extinction coefficient, ε), while the C–H and C–C stretching modes of vibration have smaller molar absorptivities. However, the symmetric stretching mode of carbon dioxide, despite the large permanent dipole between the carbon and the oxygen atoms, is infra‐red inactive because of the molecular symmetry. The changes in the electron environments from the symmetrical movement of the two oxygen atoms cancel each other out, leading to a zero overall change in dipole moment.

13.2.6.1 Infra‐red Spectrum

An infra‐red spectrum is a plot of the percentage transmittance, T (or %T), or absorbance, A, against the wavenumber (cm⁻¹). Transmittance is defined as the intensity of the IR light measured with the sample, I, ratioed against the intensity of light measured without the sample, I ₀:

13.5a

13.5b

The intensity measured without the sample is called the background spectrum. A suitable background spectrum is important because it can be used to remove spectral features that do not belong to the sample. This includes the intensity profile of the spectrometer and the absorption of IR light due to the molecules present in the atmosphere. Fluctuation in water vapour and carbon dioxide levels in the atmosphere are some of the most problematic issues in infra‐red spectroscopic measurement. Inadequate control of these will result in compromises on the quality of the sample spectrum. Modern FTIR spectrometer software is often designed with automatic atmospheric correction to remove the unwanted water vapour and carbon dioxide contribution. However, the aim should be to ensure good control of atmospheric conditions during measurements rather than to rely on subtraction of the unwanted atmospheric vapour absorbances by algorithms.

13.2.6.2 Transmittance versus Absorbance

It is advantageous to present spectra as absorbances when quantitative analysis is important because the Beer–Lambert Law states that absorbance is equal to the multiple of the concentration of samples, c, molar absorptivity, ε, and path length, l (Eq. (13.6a)). A linear relationship between absorbance and concentration is expected when the molar absorptivity and the path length are kept constant for the absorbance range of between 0 and 1. Beyond absorbance of 1, the assumption of a linear response from the detector may not hold. Absorbance is defined as the negative log of transmittance and can be used to develop standard curves for the calculation of the concentration of samples. A transmittance spectrum can be converted to an absorbance spectrum using Eq. (13.6b). Spectral peaks in an absorbance spectrum point upward with a baseline of 0 because a stronger absorption of IR light by the sample results in a higher absorbance. Spectral ‘peaks’ in transmittance, however, point downward with a baseline of 1 (or 100% if %T is used) because absorption of IR light by the sample results in a lower transmittance of light. Thus,

13.6a

13.6b

13.2.7 Raman Spectroscopy

Raman spectroscopy is a study of inelastic scattering of UV, visible or near infra‐red light. When the energy gap between the ground and the first excited electronic states is larger than the energy of the incident light, the light cannot cause an electronic excitation but it can polarise the electron cloud and induce a temporal dipole in the molecule. As the electric field of the light is oscillatory, the induced dipole in the molecule will also oscillate at the frequency of the incident light, which will then relax by emitting a photon. When the light photon is re‐emitted immediately (on the order of 10⁻¹⁵ seconds) at the same energy, and hence frequency, as the incident light, the process is called elastic scattering or Rayleigh scattering. However, the induced oscillating dipole can interact with the vibrations of the molecule and produce an oscillation in the polarisability of the molecule. The relaxation of the induced dipole can therefore be affected by the molecular vibration resulting in the molecule re‐emitting photons at a different energy and wavelength to the original incident light, as illustrated in Figure 13.1. The scattering process that results in a change in the wavelength of light due to inelastic scattering is called Raman scattering and the change in the wavelength in respect to the wavelength of the incident light is called Raman shift. If the light loses energy through the inelastic scattering process, it is called Stokes Raman scattering and if the light gains energy from the process, it is called anti‐Stokes Raman scattering. The energy diagram in Figure 13.1 shows that the difference in energy from the incidence and emitted light is dependent on the vibrational energy band gaps. Raman spectroscopy is the study of the shift in the wavelength of light through the inelastic scattering process, which shows the vibrational energy levels of the molecule. Raman scattering can only occur when the vibration induces a change in polarisability of the molecule. The selection rules for Raman scattering are therefore different to infra‐red absorption, which is one of the reasons why infra‐red and Raman spectroscopies, although both providing information on the vibrational energy levels, are complementary techniques.

13.3.1 Infra‐red Spectrometer

Infra‐red spectrometers are designed to measure the absorbance or transmittance of light through a sample at different wavenumbers in the infra‐red spectral region. The key components of an infra‐red spectrometer include an infra‐red source, a monochromator or interferometer and an infra‐red detector. The infra‐red source produces a constant flux of infra‐red radiation that covers the desired measurement range. A Globar source is often used as the black body radiator to produce a broadband light in the mid‐IR range that covers 4000–400 cm⁻¹. Some spectrometers are also equipped with a tungsten halogen lamp to produce near infra‐red light for the measurement of the near infra‐red spectrum. The infra‐red light is detected by a semi‐conductor infra‐red detector. There are different types of detector available and the selection of detector depends on the requirements of the measurement. Generally room temperature operated infra‐red detectors such as the deuterated tri‐glycine sulphate (DTGS) and the lithium tantalate (LiTaO₃) detectors are less sensitive than the liquid nitrogen cooled mercury cadmium telluride (MCT) detectors, especially at low light conditions. Furthermore, MCT detectors are available in array format, enabling the measurement of multiple spectra from different areas of the sample simultaneously. These detectors include the FPA detector and the linear array detector. Using these detectors can significantly increase the speed of data acquisition for imaging applications [1–3]. However, MCT detectors are more expensive, especially those with the array format, more easily saturated and require cryogenic cooling, which increases the running cost.

A monochromator or an interferometer is used to separate the wavelengths of light so that the intensity of infra‐red radiation at different wavelengths can be plotted individually. A dispersive infra‐red spectrometer utilises a monochromator, which consists of a diffraction grating to disperse the light and a narrow slit for wavelength selection. This type of spectrometer has become less popular because the narrow slit gives a low throughput of light. Dispersive systems also require frequent wavenumber accuracy checks or calibration to ensure that the quality of the spectrum is acceptable. Pharmacopoeias have specific requirements for the standard of performance for instruments, which must be demonstrated to validate the measurement. For infra‐red spectrometers, the performance is demonstrated through the measurement of a 35 μm thick polystyrene film. The sharpness of peaks and the wavenumber accuracy are both validated before the instrument can be used for pharmaceutical analysis.

To date, most infra‐red spectrometers are based on the use of interferometers. The interferometer splits the broadband infra‐red light beam from the source into two beams of equal intensity by means of a beam splitter. One of the beams is reflected off a fixed mirror, while the other is reflected off a scanning mirror before rejoining at the beam splitter, where the two beams interfere. The scanning mirror enables the distance travelled by the second beam to be precisely controlled so that the two beams can undergo different levels of interference depending on the wavelength of the light. A monochromatic HeNe laser beam is also shone into the interferometer where the interference pattern from the known‐wavelength laser is used to measure the differences in distance between the two optical paths (the so‐called optical path difference). The intensity measured at the position of the scanning mirror where the distances travelled by the two IR beams are equal is called the centre burst because, at this position, all wavelengths of light will be in constructive interference, resulting in the highest intensity. A plot of the scanning distance against the intensity of the IR light is called an interferogram. The intensity of light through the interferometer is the sum of all waves at different wavenumbers that created the interference pattern. Fourier transform (FT) is then applied to convert the interferogram into a single‐beam spectrum where the intensity is plotted against wavenumber. Infra‐red spectrometers that utilise an interferogram are called Fourier transform infra‐red spectrometers (FTIR).

Advantages of FTIR over dispersive systems include the lower noise and faster measurement because a slit is no longer required for wavelength selection, leading to a much higher throughput of light. FTIR spectrometers also have the multiplex advantage, which means all wavelengths are measured at the same time in contrast to dispersive systems where different wavelengths of light are measured at different times. Finally, as the optical path difference is constantly measured against the interference pattern of the monochromatic laser, wavenumber accuracy is often much better and more consistent than a dispersive system.

13.3.2 Infra‐red Sampling Protocol

There are three main measurement modes available for infra‐red spectroscopic measurements. They are the reflection mode, transmission mode and attenuated total reflection (ATR) mode. Depending on the sample, different modes of measurement can be chosen, which determines the sample preparation method. Whichever mode of measurement is chosen, a suitable background spectrum is needed. A background spectrum is obtained from a measurement made without the sample. For many cases, it is the measurement of a plain substrate (without the sample) where the sample will be deposited. For examples, a clean IR transparent window or an empty sample chamber may be used for the transmission mode or a clean reflective slide or a gold mirror is used for the reflection mode and a clean ATR element is used for the ATR mode.

13.3.2.1 Reflection Measurements

In reflection measurements, the IR light is focused on the surface of the sample with the reflected light collected by an objective or mirrors followed by measuring the intensity at the detector. Path length through the sample is not always well defined in reflection modes and therefore quantification is not always possible. There are three main types of reflection, namely specular reflection, diffuse reflection, and transflection. Depending on the physical properties of the sample, the resultant spectra can be a combined effect of the three reflections. If the sample is thin and supported on a reflective substrate, the IR light can be transmitted through the sample, reflected off the substrate and then transmitted back through the sample before being measured. This results in the measurement being dominated by the transflection mode. If the sample is highly scattering, as typically with fine powders, the measurement will be dominated by the diffuse reflection mode. If the sample is thick, non‐scattering and highly polished or the sample is a monolayer of molecule on a flat surface, the measurement will be dominated by the specular reflection mode.

Specular reflection occurs when the light interacts with the flat surface of the sample and is reflected but does not penetrate the sample (see Figure 13.3). In this case, the reflectance is dependent on the refractive index of the medium, n ₁, and the sample, n ₂, the angle of incidence and the polarisation of light. Equation (13.7) shows the reflectance, R, when the angle of incidence is 0°, which indicates that the reflectance measured is only dependent on the refractive index of the sample. A spectrum of refractive index of the sample against wavenumber is obtained. Thus,

13.7

Specular reflection is useful in the measurement of the surface of a sample or monolayers as the light only interacts with the surface layer of the sample [4]. The refractive index spectrum can be used to calculate the absorption spectrum by the Kramers–Kronig transform, which is available in most advanced FTIR spectroscopic instrument software. Samples generally require some polishing (apart from monolayer samples) to ensure that a high specular reflectance is achieved and to remove the contribution from diffused scattering.

Transflection occurs when lights penetrate into a non‐scattering sample on a highly reflective substrate (e.g. a metal surface) and then reflects off the substrate before emerging as reflected light through the sample (Figure 13.4). The reflectance is dependent on the molar absorptivity of the sample with a path length of approximately twice the thickness of the sample. However, a recent study has shown that transflection measurements may not follow the Beer–Lambert law due to the electric field standing‐wave effect [5]. Nevertheless, the method has gained popularity in the analysis of biological tissue sections due to the low cost of IR reflective low energy reflective glass slides [6]. As the IR light passes through the sample twice, the sample should be thin enough to avoid high absorbance. For tissue samples with strong protein amide bands, the ideal thickness of tissues should not be more than a few micrometres. Tissues can be embedded in an optimal cutting temperature (OCT) compound or wax block before being cryogenically microtomed to ∼5 μm thick. Tissue sections are then directly deposited on the IR reflective substrates such as the low energy reflective glass side before being measured under a microscope in reflection mode. The OCT compound can be removed by washing the tissue in 0.9% saline followed by a quick rinse in distilled water and drying in air or nitrogen before taking FTIR measurements. Wax embedding medium can be removed by washing in hexane or measured together with the tissue and then mathematically de‐waxed by spectral subtraction using spectroscopic software and algorithm [7].

In diffuse reflection, the light penetrates into the sample, is scattered and re‐emerges from the surface as scattered light. Through this process, the direction of light is lost and the radiation is absorbed by the sample. The reflectance is dependent on the molar absorptivity of the sample and the scattering efficiency. Diffuse reflectance infra‐red Fourier transform (DRIFT) is a popular technique that measures the diffused reflectance from powder samples. For example, DRIFT was used to detect melamine contamination in milk powder [8]. Powdered samples are often measured without preparation but would require an accessory specifically designed for DRIFT measurements. A DRIFT accessory typically contains a large parabolic mirror to focus the IR beam on to the powder sample and to collect the diffuse scattered light. For samples that have strong IR light absorption, samples in fine powder form can be diluted with KBr powder to lower the absorbance.

13.3.2.2 Transmission Measurements

Transmission mode measurements record the absorption of light through a sample, which can be a free‐standing film or a film placed on an infra‐red transparent substrate or a film sandwiched between two infra‐red transparent windows. The thickness of the sample defines the path length of the measurement. Samples that are in powder form, such as many pharmaceutical ingredients, can also be measured in transmission mode. One of the classical techniques for powdered sample measurement is the nujol mull method. The sample is ground into a fine powder, mixed with a small amount of nujol (paraffin oil) to form a mull. The mull is spread between two NaCl plates (or other infra‐red transparent plate) and then measured in transmission mode. Nujol, however, produces infra‐red absorbance at ∼3000–2800 and ∼1460–1360 cm⁻¹ for its CH stretching and bending vibrations, which can obscure the absorbance of the sample in these regions. For a measurement that is free from spectral interference, the powder sample can be made into a solid thin film by directly compacting between two diamond windows using a diamond cell or mixed with KBr powder (approximately 1 part of sample to 250 parts of KBr) before compacting into a KBr disc. The KBr disc can then be measured in transmission mode as a free‐standing film or on an infra‐red transparent substrate. The diamond press, Nujol mull and KBr disc methods are technically demanding and require practises for obtaining consistent, representative spectra.

FTIR imaging of biological tissues is often made in transmission mode and has shown to be a powerful method to obtain histological information without the need of staining [9]. These tissue samples can be prepared by microtoming into thin sections, as is typical in histology. However, instead of depositing the tissue sections on glass slides, they are deposited on IR transparent substrates, such as CaF₂ or BaF₂ windows. Spectral contributions from the embedding medium can be removed by washing with 0.9% saline followed by washing in distilled water if an OCT compound was used or hexane if wax was used, or influence of these materials can be removed mathematically by spectral subtraction after the measurement taken during spectral pre‐processing [7].

In transmission mode measurements, interference from the reflected light from the sample or the infra‐red window can produce a fringe pattern on the baseline of the spectrum. As illustrated in Figure 13.5 using a free‐standing film as an example, most of the IR light follows the path of beam ‘a’, which shows that the IR light passes straight through the free‐standing sample film. However, a small percentage of the IR light will follow the path of beam ‘b’, which shows the light being reflected internally before emerging from the sample. When the wavelength of light is the same as the thickness of the film (path length l) the interference between ‘a’ and ‘b’ is constructive, but when the wavelength is double the thickness of the film, the interference is disruptive. Since the mid‐IR spectrum wavelength span is from 2.5 to 25 μm, an alternation between the constructive and disruptive interference will result in a fringe pattern developed on the baseline of the measurement. The fringe pattern is weak compared to the absorbance spectrum when the refractive index of the sample, or the IR transparent window, is close to 1. However, when high refractive index materials are used, e.g. ZnSe windows, to sandwich a thin layer of sample, the fringe pattern can be significant. In this case, a wedge‐shaped window may be used to reduce the unwanted fringe pattern.

While this is an artefact from the interference between the reflected and transmitted light, it can be a useful feature to determine the path length from the fringe pattern:

13.8

13.3.2.3 Attenuated Total Reflection (ATR)

The ATR mode is a highly versatile method that is suitable to measure solid and liquid samples with little sample preparation required. In this measurement mode, a high refractive infra‐red transparent material (often referred as an ATR crystal if a crystal is used or more generally as an internal reflection element, IRE) is needed to generate an internal reflection at the sample–IRE interface. A common approach is to shine infra‐red light to the IRE element from below towards the sampling surface at an incident angle that is greater than the critical angle, as illustrated in Figure 13.6. When the IR light is internally reflected, it penetrates into the sample by a few micrometres as an evanescence wave, as shown in Figure 13.6, which can be absorbed by the sample. The measurement of this absorption of light produces an ATR spectrum. The strength of the evanescent wave is strongest at the interface, which decays exponentially into the sample. The distance from the interface to where the evanescent wave decays to e ⁻¹ (∼37%) is defined as the depth of penetration, d _p :

13.9

Equation (13.9) shows that the depth of penetration is a function of the wavelength of light, the refractive indices of the sample and the IRE and the angle of incidence, θ. These are the important parameters for the ATR measurement mode. For example, the different bands in a spectrum will have a different d _p depending on the wavelength of the band. Nevertheless, a typical ATR measurement produces a d _p of a few micrometres; therefore the ATR mode is often considered as a surface layer measurement technique. With the small value of d _p and the exponential decay in the strength of the evanescence wave, only the surface layer of the sample that is a few micrometres from the IRE is measured. A good contact between the IRE and the sample is important because an air gap as small as 1 μm between the sample and the IRE will result in a significant drop in the absorbance and invalidates the Beer–Lambert law. Many commercial ATR accessories have a pressure transducer sample press integrated above the measuring surface of the IRE so that a known reproducible pressure can be applied to compress the sample. Measurements of powder samples can be made without sample preparation by directly compressing a small amount of the powder on to the ATR element surface. FTIR measurements in the ATR mode were used in research to investigate the effect of composition in pharmaceutical formulation on the density of the compacted powder [10]. For the measurement of a liquid sample, intimate contact is achieved without the need of a press. However, a glass cover may be used to reduce evaporation of samples during measurement, especially when the liquid is volatile.

Although the Beer–Lambert law applies in ATR measurements, the path length is not as clear as in transmission measurements. The effective path length (also known as the equivalent path length) is the path length in transmission mode that would produce the same absorbance in an ATR mode measurement. It is also an important parameter to be considered for the design of an ATR experiment. The effective path length of an ATR measurement can be calculated using the following equations [11]:

13.10a

where de(S) and de(P) are the effective path lengths for the s‐ and p‐polarised lights. For a non‐polarised light, the effective path length will be the average of de(S) and de(P). It is important to note that the effective path length for ATR measurements does not have a physical reference of the distance the light travelled in the sample because light interacts with the sample through the evanescent wave. An important feature of an ATR spectrum is that the effective path length and the depth of penetration become smaller towards the higher wavenumber region. Another feature of an ATR spectrum is, from Eqs. ( 13.9), (13.10a) and (13.10b), that the effective path length and the depth of penetration are dependent on the refractive indices. This can lead to the spectral bands measured in the ATR mode being slightly red‐shifted compared to the same spectrum measured in transmission mode. This is due to the dispersion of the refractive index of the sample near the absorption band. If the angle of incidence is close to the critical angle, for example, in the measurement of minerals enclosed in tissues [12], a derivative‐like baseline near the absorption bands of the ATR spectrum can result. In this case, a higher refractive index IRE, such as germanium, which has a refractive index of 4, should be used. Some ATR accessories would allow the angle of incidence to be increased to avoid such a situation [13].

13.3.2.4 Multireflection ATR

The effective path length of a single reflection ATR measurement is typically below 2 μm, which is suitable for measuring highly absorbing substances such as water. However, for the measurement of weaker spectral bands or when the concentration of the solute of interest is low, increasing the path length would increase the absorbance to enable the detection and quantification of substances at lower concentrations [14]. In transmission mode, the path length can be adjusted by changing the thickness of the sample. In ATR mode, the path length can be increased by increasing the number of internal reflections on the sample using a multireflection (also called multibounce) ATR accessory. The schematic in Figure 13.7 shows a typical multireflection ATR accessory with a trapezoid ATR element. A recent study has shown that an optimised multireflection ATR measurement can improve the limit of detection from the mM level to approximately 20 μM in aqueous solution [14], significantly increasing the number of potential applications of attenuated total reflection Fourier transform infra‐red (ATR‐FTIR) studies, especially in biology where many compounds of interest are at low concentrations.

13.3.3 Raman Scattering

13.3.3.1 Spontaneous Raman Scattering

Spontaneous Raman scattering is a weak scattering process with signals approximately three orders of magnitude weaker than Rayleigh scattering. The intensity of the Raman scattering light, I _R , from a sample is related to the intensity, I ₀, and the frequency, ν ₀, of the illuminating light source through the following relationship:

13.11

where ν _vib is the frequency of the molecular vibration. Using a high intensity light source can improve the Raman scattering signal. Most Raman spectrometers are therefore equipped with lasers as the monochromatic light source. However, increasing the intensity of illumination raises the risk of overheating of the sample. In some cases, samples can be burnt, vaporised or chemically degraded during measurement. Strategies to reduce the heat from the intense illumination include immersing the sample in water during measurement (using a water immersion objective) or spreading out the intensity of the laser from a spot to a line [15] or multiple spots by microlens array with fibre optics bundles [16]. The latter method also enables the collection of multiple spectra simultaneously, which can significantly increase the speed of data collection [17].

Some of the typical wavelengths used include 478, 514, 633, 785, 830 and 1064 nm. In the earlier studies, 785 and 830 nm lasers were the two most popular choices for biological specimen studies due to the lower risk of fluorescence and photo damage. For example, melanin can be measured with an 830 nm laser [18] but not with shorter wavelength lasers. However, longer wavelength lasers produce a weaker Raman signal when compared to shorter wavelength lasers and therefore require higher power and a longer acquisition time. To date, lasers of shorter wavelength are also used for biological applications when the sample does not fluoresce.

13.3.4 Raman Spectrometer

A Raman spectrometer is designed to measure the intensity of the inelastic scattered light (i.e. the Raman signal) from a monochromatic laser. The measurement can be made using a dispersive system or an FT system. However, dispersive systems are more common than FT systems for Raman spectroscopy because dispersive Raman systems generally have a higher sensitivity than FT Raman systems. In a dispersive system, the scattered light collected from the sample is first passed through a filter (either a notch filter or an edge filter) that removes the laser line followed by shining the light on a diffraction grating to separate the wavelengths of the scatter light before being focused on the highly sensitive array detector (e.g. a Peltier cooled charge‐coupled device [CCD] array detector). The different pixels on the array detector simultaneously measure the intensity of the Raman signal at different wavelengths from the dispersed light. The spectral resolution of the measurement is dependent on the type of grating used, the number of pixels the array detector has and the wavelength stability of the laser. A typical research Raman spectrometer would have a CCD camera containing a large number of pixels to measure the Raman signal at different wavelengths so that a full spectrum (e.g. from 3800 to 100 cm⁻¹) can be measured in one snapshot. However, changing the spectral resolution involves a change of hardware and alignments, which are mostly automated in modern systems. A Fourier transform Raman (FT‐Raman) system utilises the same principles as the FTIR to separate the Raman intensity at different wavelengths. FT‐Raman systems utilise a 1064 nm laser as the excitation light source such that the chance of sample fluorescence is minimised. However, the long excitation wavelength used in an FT‐Raman system will produce a weaker Raman signal, according to Eq. (13.11), when compared to a dispersive system that uses a shorter excitation wavelength. To compensate for the weaker signal, a highly sensitive liquid nitrogen cooled germanium detector is used in an FT‐Raman system and the measurements, generally, are slower than measurements made with a dispersive system.

As discussed above, the intensity from the Rayleigh scattering is much stronger than the weak Raman scattering and the laser line must be filtered before it reaches the detector. This can be done by either the use of an edge filter or a notch filter. The aim of these filters is to reduce the intensity of the Rayleigh line to a level that is similar or lower than the Raman lines so that the Rayleigh line does not overwhelm the signal of the Raman lines. Special filters have an extremely sharp cut‐off transmittance profile so that Raman signals a few wavenumbers above the Rayleigh line can be measured are now available. This region of the spectrum, ∼5–150 cm⁻¹ is called the low frequency region (or far‐IR spectrum if infra‐red absorption is measured). The low frequency region can provide information on intermolecular forces. As a result, it is highly sensitive to the changes in the intermolecular structure and, therefore, is suitable to study transitions between amorphous and crystalline forms and changes in molecular mobilities in amorphous (glassy) materials. The study of pharmaceutical materials in the low frequency region has helped in the understanding of amorphous solid drug dispersion in a glassy matrix and the prediction of the stability of amorphous drug systems [27].

13.3.5 Raman Sampling Protocol

Most Raman measurements are acquired in backscattering mode, which means little sample preparation is required. A simple lens or objective can be used to focus the laser beam on to the sample, which can be a pharmaceutical tablet, drug powder, polymer blocks or films, tissue cross‐sections or cells. The same objective or lens can be used to collect the backscattered light for detection. Raman spectra may be collected though containers or packages if the walls of the container or packages are transparent to the light in the range of the excitation laser used. Fibre optic probes are another well‐developed technique for Raman spectral data collection. It is particularly useful for collecting spectra from a large object or remotely from a pipeline or reactor in a processing plant. In contrast to infra‐red, fibre optics and probes in the visible range are widely available at a much lower cost. Some Raman instruments have fibre optics to transfer light between the spectrometer and the microscope with minimal loss in light intensity.

Raman spectra acquisitions generally do not require the collection of a background spectrum as it is a scattering technique rather than an absorption technique. However, some instruments offer the option of taking a background measurement, which is a measurement with the laser beam blocked or switched off. The subtraction of this background spectrum from the measurement can reduce the pixel to pixel variations along the detector array. More importantly, the detector used in a Raman spectrometer is highly sensitive to visible light. Stray light from the environment can produce spectral artefacts and increase background noise. The sample compartment and the collection optics of the instrument should be enclosed during data collection or the measurement should be collected in the dark.

As the scattered light is random in direction, a large NA objective is beneficial for maximising the amount of signal collected. A higher NA microscope objective with higher light collection efficiency will produce better Raman spectra than a lower NA objective. When a microscope with high magnification objectives is used to illuminate and collect the light, the measurement is called Raman microspectroscopy or simply Raman microscopy. If the microscope has a motorised stage or the mirror that directs the laser to the objective is motorised, Raman images can be obtained by rastering the sample point by point or line by line. The higher the magnification and the higher the NA the objective used, the smaller the laser spot will be generated and the better the lateral spatial resolution can be achieved. Since UV, visible or NIR lasers are used as the illuminating source, the spatial resolution obtained in Raman mapping is similar to UV, visible and NIR imaging. Note that Raman mapping may be referred as Raman imaging in the literature, especially when the speed of mapping is fast relative to the movement of the sample. For dynamic systems, such as living samples, the data acquisition rate will need to be sufficiently high so that there will be negligible movement of the sample within the imaged area for the duration of the imaging measurement. The lateral spatial resolution can be estimated using the Rayleigh criterion (Eq. (13.12)), where r is the distance between two adjacent points that are considered just resolved:

13.12

In contrast to non‐linear Raman such as SRS and CARS, the intensity of spontaneous Raman generally has a linear relationship with the intensity of the incident light so that the molecules in the volume above and below the focus can produce significant contributions to the overall Raman spectrum. This can result in a poor axial resolution for the measurement. To improve the axial resolution, a confocal microscope is used. A confocal microscope comprises a microscope objective with a pin‐hole aperture. The pin‐hole allows the scattered light from the focus of the illumination to pass thought to the detector while blocking light from other layers of the sample, as illustrated in Figure 13.8. Systems with fibre optics to transfer light between the microscope and the spectrometer are inherently confocal because the narrow entrance of the fibre optics produced the same effect as the pin‐hole aperture. With the confocal setup, depth profiling (also called optical sectioning) of the sample can be achieved without cutting the sample, which is highly desirable for biological applications. One important point to note when performing depth profiling using the confocal mode is that an immersion objective should be used instead of a dry objective. A liquid medium (e.g. oil or water, depending on the type of immersion objective used) is added to the gap between the sample and the objective to reduce the refraction of light as it enters or exits the sample. Without the oil immersion objective, the actual sampling depth will be approximately twice the apparent depth and the axial resolution will be significantly degraded as a result of refraction of the laser at the sample–air interface [28].

When measuring a new sample with a Raman spectrometer or microscope, measurement parameters should be first optimised. The laser power should be first adjusted to a low setting (e.g. 1% power) to test if the sample will burn under this level of power. The laser power can then be slowly increased with the spectrum of the sample monitored over a period of exposure time to detect thermal degradation of the sample. Burnt organic samples can be detected by observing the appearance of the broad D and G bands of amorphous carbon at ∼1350 and 1595 cm⁻¹, respectively. If a sample is sensitive to heat and is burnt by the laser, a lower laser power should be used. The highest laser power should only be used to maximise the Raman signal if the sample is stable. If the sample fluoresces, which produces an intense and broad baseline shift, the sample may be exposed in the laser while continuously acquiring spectra to observe if the fluorescence signal can be decreased by photo‐bleaching. This procedure can be effective if the fluorescence signal originates from impurities or minor components in the sample that are not of interest in the study. However, if the fluorescence signal does not reduce by photo‐bleaching, or if samples are sensitive to the strong illumination of light, as with many biological materials, a laser with a longer wavelength should be used instead. Sample heterogeneity can be an issue when high magnification objectives ar used. In this case, measurements from several different areas of the sample or a hyperspectral image should be obtained to ensure that the spectra measured represent the bulk composition.

13.4.1 Case Study 1: Drug Polymorph Studies

Polymorphism in pharmaceutics is a term used to describe a drug solid that can exist in more than one crystalline form. A change in the crystalline structure can have pronounced effects on many physical properties of the drug that are important to the manufacturing process, such as particle shape and melting point, as well as the performance of the pharmaceutical product, such as the dissolution rate. The study of drug polymorphism is, therefore, an important area in pharmaceutical research and drug development. Vibrational spectroscopy has been an important analytical tool for this purpose. Although the chemical structure of the molecule remains the same in the different crystalline forms, changes in the molecular environment due to the different molecular arrangements could lead to observable differences in the vibration spectrum. Chemical bonds can be weakened or strengthened when intermolecular bonds are formed or broken. The changes in the bond strength, according to Eq. ( 13.3), will result in a shift in the wavenumber of the spectral band, allowing the different polymorphs of a drug to be distinguished and the functional group involved in the interaction to be identified. FTIR and Raman have become powerful tools in the development of pharmaceutical formulations and monitoring tools for process control [39,40].

Polymorphic transition of crystalline materials, whether intentional or unintentional, can happen during manufacturing processing such as milling, granulation and extrusion. Accidental polymorphic conversion of a crystalline drug can affect the manufacturing process and results in out‐of‐specification products. Online monitoring using FTIR and Raman can be used to study changes in the polymorph in the manufacturing process to reduce problems associated with the changes in the physical properties of a drug. A recent study [41] has employed both in situ FTIR and in‐line Raman to monitor the polymorphic transition of caffeine in a twin‐screw melt granulator and in a rheometer. The results show that both Raman and FTIR have detected the conversion of caffeine from form II to I when heated in both the hot melt granulator and the rheometer, demonstrating that the rheometer can be used as a simulator for the hot melt granulator process studies.

While vibrational spectroscopy can often identify the different polymorphs, the limit of detection of these techniques is relatively poor compared to powder X‐ray diffraction methods. For example, a study on the polymorphism of the drug imatinib has found that although the spectrum of α‐ and β‐crystalline [42] could be easily distinguished by FTIR, the lack of a characteristic band of β‐crystalline resulted in a rather poor limit of detection and, in comparison, powder X‐ray diffraction was found to provide the best limit of detection for that particular system. Nevertheless, the advantages of vibrational spectroscopy over other analytical techniques, such as non‐destructive measurements, non‐invasiveness, low cost equipment and the technology can be adapted for online measurement, should be considered.

13.4.1.1 Amorphous Drug Studies

Molecules in amorphous solid drugs, in contrast to crystalline drugs, do not have long‐range order. Instead, molecules have only short‐range order, which can lead to profound differences in the physical properties of the drug. For example, due to the overall weaker molecular interactions for amorphous solids, the dissolution rate of an amorphous solid can be orders of magnitude higher than the crystalline form [43,44]. This provides an opportunity to prepare drugs in amorphous form to harness the advantage of the improved dissolution rate. However, amorphous solids are thermodynamically unstable and they will eventually crystallise into the more stable forms. To date, difficulties in manufacturing process, poor amorphous stability and hard‐to‐predict crystallisation remain some of the key barriers for the wider use of amorphous drug in the pharmaceutical industry.

Since molecules in amorphous solids have only a short‐range order, vibrational spectral bands of amorphous solids are significantly broader when compared to their crystalline counterparts. Raman and FTIR spectroscopy can be applied to distinguish amorphous form from their crystalline forms by the differences in the shape and position of the bands. For examples, amorphous and crystalline nifedipine were found to have distinct spectra (see Figure 13.9). An in situ Raman study of the crystallisation of amorphous nifedipine has shown that the drug first crystallised into the meta stable β‐crystalline form before converting into the most stable α‐crystalline form when exposed to high relative humidity and 40 °C (near the T _g ) [45]. Raman mapping was also applied to detect trace crystalline griseofulvin and fenofibrate in solid dispersion prepared by hot‐melt extrusion [46]. It was found that when combined with chemometric analysis, small drug crystals a few micrometres in length can be detected within the amorphous formulation. In another study, the stabilities of co‐amorphous nifedipine–nitrendipine systems at different drug ratios have been compared using FTIR imaging [47], where it has been shown that the 1 : 1 drug ratio has the best amorphous stability. Apart from detecting drug crystallisation in amorphous formulations, Rumondor et al. [48] have used FTIR to study the mechanism of amorphous drug recrystallisation in a polymer‐drug amorphous solid solution system. Using the peak position of the N–H stretching mode vibration of nifedipine, they have deduced that the drug crystallised by first phase separating into amorphous drug‐rich regions before crystallising. More recently, amorphous and crystalline nifedipine in different formulations of PEG and PVP were identified by FTIR spectroscopy, showing that vibrational spectroscopic methods are useful tools for studying recrystallisation of amorphous drugs [ 43,49]. For further reading on the applications of infra‐red and Raman spectroscopies on amorphous drugs, a comprehensive review on this topic can be found in [50].

13.4.2 Case Study 2: Live Cell Analysis

Cell‐based assays form a large part of biological and medical research. However, bioanalyses of cells often require cell lysing or the addition of molecular probes that may disrupt the natural cellular environments or produce unwanted measurement artefacts. Fortunately, the majority of the cellular components, such as water, protein, lipids, carbohydrates, nucleic acids, are all directly detectable using vibrational spectroscopic techniques. The highly chemically specific, non‐destructive and non‐invasive nature of vibrational spectroscopic methods have become attractive analytical tools for live cell studies [34].

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Further Reading

1. Salzer, R. and Siesler, H.W. (2014). Infrared and Raman Spectroscopic Imaging, 2nd, Completely Revised and Updated Edition. ISBN: 978‐3‐527‐33652‐4.
2. Sasic, S. and Ozaki, Y. (2011). Raman, Infrared, and Near‐Infrared Chemical Imaging. Wiley.
3. Schlücker, S. (2011). Surface Enhanced Raman Spectroscopy: Analytical, Biophysical and Life Science Applications. Wiley‐VCH Verlag GmbH & Co. KGaA. ISBN: 9783527325672, Online ISBN:9783527632756, https://doi.org/10.1002/9783527632756.
4. Siebert, F. and Hildebrandt, P. (2008). Vibrational Spectroscopy in Life Science. Wiley‐VCH Verlag GmbH & Co. KGaA. ISBN: 9783527405060, Online ISBN: 9783527621347, https://doi.org/10.1002/9783527621347.