RAMAN SPECTROSCOPY

Introduction

A large variety of spectroscopic techniques are available for the analysis of materials and chemicals. Among these is Raman spectroscopy. This relies on Raman scattering of light by a material, where the light is scattered inelastically as opposed to the more prominent elastic Rayleigh scattering. This inelastic scattering causes shifts in wavelength, which can then be used to deduce information about the material. Properties of the material can be determined by analysis of the spectrum, and/or it may be compared with a library of known spectra to identify a substance.

Since the discovery of Raman scattering in the 1920s, technology has progressed such that Raman spectroscopy is now an extremely powerful technique with many applications.

Raman scattering

Raman scattering (sometimes called the Raman effect) is named after Indian physicist C. V. Raman who discovered it in 1928, though predictions had been made of such an inelastic scattering of light as far back as 1922. The importance of this discovery was recognised even then, and for his observation of this effect Raman was awarded the 1930 Nobel Prize in Physics. This was and remains the shortest time from a discovery to awarding of the Prize. In fact Raman was so confident that he arranged his travel to Stockholm several months in advance of the recipients being announced! This confidence seems quite justified, given that within a year and a half of his discovery, more than 150 papers mentioning the effect had been published. Since then Raman scattering has given rise to a number of important technologies, and foremost among these is Raman spectroscopy.

Most light passing through a transparent substance undergoes Rayleigh scattering. This is an elastic effect, which means that the light does not gain or lose energy during the scattering. Therefore it stays at the same wavelength. The amount of scattering is strongly dependent on the wavelength, being proportional to λ^-4. (It is this fact that makes the sky blue, the shorter wavelength blue components in the Sun’s light are Rayleigh scattered in the atmosphere far more than the longer wavelengths. Blue light is then seen coming from all over the sky. The scattering of blue light from its direct path from the Sun also causes the Sun itself to appear yellow.)

In Rayleigh scattering a photon interacts with a molecule, polarising the electron cloud and raising it to a “virtual” energy state. This is extremely short lived (on the order of 10^-14 seconds) and the molecule soon drops back down to its ground state, releasing a photon. This can be released in any direction, resulting in scattering. However since the molecule is dropping back to the same state it started in, the energy released in the photon must be the same as the energy from the initial photon. Therefore the scattered light has the same wavelength.

Raman scattering is different in that it is inelastic. The light photons lose or gain energy during the scattering process, and therefore increase or decrease in wavelength respectively. If the molecule is promoted from a ground to a virtual state and then drops back down to a (higher energy) vibrational state then the scattered photon has less energy than the incident photon, and therefore a longer wavelength. This is called Stokes scattering. If the molecule is in a vibrational state to begin with and after scattering is in its ground state then the scattered photon has more energy, and therefore a shorter wavelength. This is called anti-Stokes scattering.

Three different forms of scattering

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Only about 1 in 10⁷ photons undergo Stokes Raman scattering and so this is usually swamped by the far more prominent Rayleigh scattering. The amount of anti-Stokes scattering is even less than this.

The shift due to the Raman effect is determined by the spacing between the vibrational states and the ground states i.e. by the phonons of the system. The Stokes and anti-Stokes scattered light will be shifted an equal distance on opposite sides of the Rayleigh scattered light. Therefore the spectrum is symmetrical about the wavelength of light used, apart from the difference in intensities.

Normally in Raman spectroscopy only the Stokes half of the spectrum is used, due to its greater intensity.

In one of Raman’s experiments demonstrating inelastic scattering he used light from the Sun focused using a telescope to obtain a high intensity light. This was passed through a monochromatic filter, and then through a variety of liquids where it underwent scattering. After passing through these he observed it with a crossed filter that blocked the monochromatic light. Some light was seen passing through this filter, which showed that its wavelength had been changed.

Comparison with other types of spectroscopy

It is instructive to compare the process of Raman scattering with some other spectroscopic techniques. In the commonly used infrared absorption spectroscopy, infrared light excites certain vibrational frequencies of molecules and is absorbed by them, not re-emitted. This gives an absorption spectrum, with bands at characteristic wavenumbers. Other absorption techniques use higher energy radiation (e.g. ultraviolet) and raise electrons to an excited state.

Fluorescence occurs when light (often UV) is incident on a molecule and promotes an electron to an excited state. The molecule is also vibrating. Firstly it relaxes from its vibrational state, dissipating this energy (normally as heat). Then when it drops back down to the ground state, the photon released has less energy than the incident photon. The increased wavelength often means that the light is now in the visible region. This is how fluorescent lighting works, by ionisation of mercury to produce UV light, which is then absorbed by a fluorescent coating and re-radiated as visible light. Fluorescence can also be used for spectroscopy.

Below is an overview of some different interactions of light with a molecule.

Raman active modes

The Raman shift depends on the energy spacing of the molecules’ modes. However not all modes are “Raman active” i.e. not all appear in Raman spectra. For a mode to be Raman active it must involve a change in the polarisability, α of the molecule i.e.
 where q is the normal coordinate and e the equilibrium position.

This is known as spectroscopic selection. Some vibrational modes (phonons) can cause this. These are generally the most important, although electronic modes can have an effect, and rotational modes may be observed in gases at low pressure.

The spectroscopic selection rule for infrared spectroscopy is that only transitions that cause a change in dipole moment can be observed. Because this relates to different vibrational transitions than in Raman spectroscopy, the two techniques are complementary. In fact for centrosymmetric ( centre of symmetry ) molecules the Raman active modes are IR inactive, and vice versa. This is called the rule of mutual exclusion.

The origin of Stokes and anti-Stokes scattering due to vibrational modes can be explained in terms of the oscillations involved. The polarisability (α) of the molecule depends on the bond length, with shorter bonds being harder to polarise than longer bonds. Therefore if the polarisability is changing then it will oscillate at the same frequency that the molecule is vibrating (ν_vib).

Polarisability of the molecule:

There is an external oscillating electric field from the photon, with a frequency ν_p:

E = E₀ sin( 2 π ν_p t)

Therefore the induced dipole moment is:    

Using the trigonometric identity:

The induced dipole moment is:

A dipole moment oscillating at frequency ν results in a photon of frequency ν. Therefore in this case there are photons scattered at frequency ν_p (Rayleigh scattering), ν_p – ν_vib (Stokes scattering) and ν_p +ν_vib (anti-Stokes scattering).

Of course if the polarisability is not changing then the dipole moment will simply oscillate at frequency ν_p, and only Rayleigh scattering will occur. This is the origin of the spectroscopic selection rule for Raman scattering.

The Raman (and IR) activity of more complicated molecules can be determined using their symmetry and group theory, which goes beyond the scope of this TLP. There are links to more information in the Going further section.

The above is based on single molecules in a gas, and hence not interacting with neighbours. In materials science Raman techniques are more often used for solids, where molecules cannot be taken individually. In crystalline materials vibrations are quantised as phonons, modes determined by the crystal structure. The spectroscopic selection rule still applies, i.e. only phonons with a change in polarisability are Raman active. Phonons are generally of a lower frequency than the vibrations in gases, so result in lower wavenumber shifts. Structural information can therefore be determined from these shifts.

Crystal orientation can also be determined from the polarization of the scattered light.

Method (dispersive Raman spectroscopy)

Portable Raman spectrometer, as used at NASA (NASA usage guidelines)

Raman used light from the Sun focused through a telescope to achieve a high enough intensity in his scattered signal. Modern spectrometers use both improved sources and more sensitive detectors to obtain better results. Early spectrometers used mercury arc lamps as a light source. Now lasers are normally employed due to their high intensity, single wavelength and coherent beam.

Initial spectrometers used photographic plates to detect the light. The advent of more sensitive photomultiplier tubes led to their widespread use, allowing the data to be collected and manipulated electronically. However they had the disadvantage of only being able to count one wavelength at a time. Modern spectrometers use charge-coupled devices (CCDs) that combine the advantages of the previous techniques, being highly sensitive, electronic, and able to measure a whole spectrum at once.

The chief difficulty in Raman spectroscopy is preventing overlapping of the Raman signal by stray light from the far more intense Rayleigh scattering. Interference notch filters are commonly used, which filter out wavelengths within approximately 100 cm^-1 of the laser wavelength. However these are obviously of no use for studying low Raman shifts (e.g. those produced by low frequency phonons) within this region. One improvement is to use multiple stages for dispersion, with either double or triple spectrometers. Holographic diffraction gratings can be used which result in much less stray light than ruled ones. 

A simplified diagram of a Raman spectrometer’s operation is shown below.

An important consideration in Raman spectroscopy is the spectral resolution, the ability to resolve features within the spectrum. There are two ways to increase spectral resolution, by increasing the focal length or by changing the grating used to disperse the spectrum. Doubling the focal length approximately doubles the spectral resolution. Similarly doubling the density of lines on the grating results in twice the dispersion and twice the spectral resolution. However higher density gratings have restricted working ranges e.g. a grating with 2000 lines per mm cannot be used for infrared work.

The choice of wavelength used is important, and can range from the near infrared into the ultraviolet. As already mentioned the choice may be limited by the density of the diffraction grating. In addition for materials that show fluorescence it is vital to choose a longer wavelength that will minimise fluorescence, as otherwise this will swamp the weak Raman effect. However, higher energy ultraviolet lasers can be useful for penetrating certain samples where fluorescence is not a problem. Another consideration is that visible lasers are generally easier to work with. These varying factors mean that many spectrometers have a number of lasers, which can be switched as appropriate. Of course different lasers will require different filters to remove the Rayleigh scattered light.

Raman microspectroscopy

Raman spectroscopy can also be used for microscopic analysis and imaging. There are two main methods: direct imaging and hyperspectral imaging (chemical imaging).

Direct imaging involves examining the whole sample for characteristic shifts e.g. of a single compound. This generates an image showing the distribution of that compound.

In hyperspectral imaging Raman spectra are taken at points across the sample, so that multiple compounds and their distributions can be identified. The disadvantage is that with a spectrum taken for every pixel, this requires a lot of computing power and storage space.

The instrument in the Department of Materials Science & Metallurgy, University of Cambridge, is a typical microspectrometer, manufactured by Renishaw.

An interactive diagram of this is shown below, to give a feel for the components and operation. Hover over components to see a description of them, and click 'Play' to see the path that light takes through the spectrometer.

Alternative techniques

Fourier transform (FT) Raman

Unlike dispersive Raman spectroscopy, which obtains a spectrum by diffraction of the different wavelengths, Fourier transform (FT) Raman creates an interference pattern that can be analysed to recover the spectrum. It has the advantage of being faster than the dispersive technique, but is limited in resolution and choice of laser wavelength.

Stimulated Raman

Stimulated Raman scattering is a non-linear phenomenon that results in a much larger Raman signal than standard scattering (4 to 5 orders of magnitude greater). It can be triggered with a strong laser pulse. Only the strongest Raman active mode is excited at first, but scattering from it can be strong enough to excite the second mode, which in turn can excite the third and so on in a cascade effect.

Diagram of Stimulated Raman

Resonance Raman

Another effect that greatly increases the magnitude of scattering is Resonance Raman (RR). This occurs when the energy of the incident radiation is close to that of an electronic excitation energy (i.e. the band gap). Tunable lasers can be used to achieve this. The Raman scattering of vibrational modes around this excited state is then greatly enhanced by resonance effects.

Surface Enhanced Raman Spectroscopy (SERS)

Surface Enhanced Raman Scattering (SERS) is a process that can occur when samples are adsorbed on gold or silver surfaces. It results in a vast increase in the Raman effect, and is therefore useful for spectroscopy. Though the mechanism is not very well understood, it is believed to be a combination of chemical enhancement of polarisability by bonds formed between the sample and the surface, and electromagnetic resonance of small gold or silver particles. This effect can be combined with Resonance Raman for Surface Enhanced Resonance Raman Spectroscopy (SERRS), which results in very strongly enhanced signals, up to 1014 times more intense than standard Raman scattering.

Coherent Anti-Stokes Raman Spectroscopy (CARS)

Coherent Anti-Stokes Raman Spectroscopy (CARS) is a technique involving two lasers. One is of a fixed frequency ν₁ and the other is tunable to a lower frequency ν₂. When combined they result in coherent radiation at frequency

ν' = 2 ν₁ - ν₂

along with a number of other frequencies.

If there is a Raman active mode with characteristic frequency νm, then when the second laser is tuned such that

ν₂ = ν₁ - ν_m

then the coherent emission emerges in a high intensity narrow beam with frequency

ν' = 2 ν₁ - ( ν₁ - ν_m) =  ν₁ + ν_m

This is the anti-Stokes frequency, hence the name.

Diagram of Coherent Anti-Stokes Raman Spectroscopy

Raman optical activity – compares polarisations

Raman optical activity is a technique which compares the different polarisations of Raman scattered light from chiral molecules such as those found in biology, in order to determine more about their structure. This can also be combined with amplifying techniques such as resonance and surface enhancement.

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Advantages and disadvantages

Advantages...

Raman spectroscopy has a number of advantages over other analysis techniques.

• Can be used with solids, liquids or gases.
• No sample preparation needed. For infrared spectroscopy solids must be ground into KBr pellets or with nujol to form a mull.
• Non-destructive
• No vacuum needed unlike some techniques, which saves on expensive vacuum equipment.
• Short time scale. Raman spectra can be acquired quickly.
• Can work with aqueous solutions (infrared spectroscopy has trouble with aqueous solutions because the water interferes strongly with the wavelengths used)
• Glass vials can be used (unlike in infrared spectroscopy, where the glass causes interference)
• Can use down fibre optic cables for remote sampling.

...and disadvantages

• Cannot be used for metals or alloys.
• The Raman effect is very weak, which leads to low sensitivity, making it difficult to measure low concentrations of a substance. This can be countered by using one of the alternative techniques (e.g. Resonance Raman) which increases the effect.
• Can be swamped by fluorescence from some materials.

Applications

There are a huge number of applications of Raman spectroscopy. Below are a few notable examples.

Measuring/mapping stress

Raman spectroscopy can be used to measure stress and strain in materials. Tensile strain increases the length of the bonds and the tension in them, hence changing the frequency of the phonons. It therefore causes a shift in the observed Raman bands towards lower wavenumbers.

Forensics, explosives/drugs detection

Photo of Raman integrated tunable sensor from Oak Ridge National Laboratory site. (See their copyright notice)

Advances in technology have led to much smaller spectrometers, which are moving from the laboratory bench towards handheld devices that can be used for analysis in the field. They may be linked to a library of spectra, and can be used by law enforcement and customs officials to detect explosives, drugs and other chemicals. They are also useful for quickly identifying possibly hazardous materials e.g. after a spillage.
Pictured is a Raman integrated tunable sensor (RAMITS) developed by the US government. It has a probe coated with silver nanoparticles, which allow Surface Enhanced Raman Spectroscopy, boosting the signal. The instrument is handheld and battery powered.

Process monitoring

Raman spectroscopy is a non-destructive process, and can be used to monitor industrial processes. The speed of analysis means that it can give almost real-time information. Another advantage is that the light to be monitored can be sent down fibre-optics, so that the Raman equipment can be located some distance away from the actual processing.

Uncovering artistic techniques

A page from the book of Kells - in the public domain from Wikimedia Commons

As well as monitoring state of the art processes, Raman spectroscopy is being used to uncover the secrets of ancient artefacts. Scientists at Trinity College in Dublin are using Raman spectroscopy to examine the famous Book of Kells, an illustrated manuscript dating from the 9th century. They hope to determine the composition and origins of the paper, inks and pigments used, which will tell them about techniques used and trade routes of the age.

Life on Mars

Raman spectroscopy could also be used to search for life on Mars. Modern Raman technology has been miniaturised to the point that a small spectroscope will be carried on a future mission to the planet. The instrument will be used to look for evidence of life and/or life supporting conditions either in the present or the distant past, as well as more general analysis of the Martian surface. Similar instruments could be featured on missions to other potential sites of life such as Europa or Callisto.

Carbon nanotubes

Because of their structure, carbon nanotubes can be made to resonate with light. They may resonate with either the incident wavelength, or Raman scattered wavelengths. Resonance can also occur for a number of different modes. Some of the most important are the radial breathing mode, the disorder mode and the high energy mode.

Observations of these can be used to determine important properties of the nanotubes, such as their diameter and strain. Raman spectroscopy is one of the easiest ways of measuring these vital properties.

Summary

Raman scattering is the inelastic scattering of light. It is caused by light interacting with molecules that have a changing polarisability, often due to vibrations. It forms the basis of Raman spectroscopy, where the shifts in wavelength are used to determine modes of a sample, which can be solid, liquid or gas. These modes can be vibrational (e.g. phonons), rotational or other low frequency modes. Raman spectroscopy is an important technique that is now used in a wide variety of applications.

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CHROMATOGRAPHY...... Introductory theory

Introduction

Few methods of chemical analysis are truly specific to a particular analyte. It is often found that the analyte of interest must be separated from the myriad of individual compounds that may be present in a sample. As well as providing the analytical scientist with methods of separation, chromatographic techniques can also provide methods of analysis.
Chromatography involves a sample (or sample extract) being dissolved in a mobile phase (which may be a gas, a liquid or a supercritical fluid). The mobile phase is then forced through an immobile, immiscible stationary phase. The phases are chosen such that components of the sample have differing solubilities in each phase. A component which is quite soluble in the stationary phase will take longer to travel through it than a component which is not very soluble in the stationary phase but very soluble in the mobile phase. As a result of these differences in mobilities, sample components will become separated from each other as they travel through the stationary phase.
Techniques such as H.P.L.C. (High Performance Liquid Chromatography) and G.C. (Gas Chromatography) use columns - narrow tubes packed with stationary phase, through which the mobile phase is forced. The sample is transported through the column by continuous addition of mobile phase. This process is called elution. The average rate at which an analyte moves through the column is determined by the time it spends in the mobile phase.

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Distribution of analytes between phases

The distribution of analytes between phases can often be described quite simply. An analyte is in equilibrium between the two phases;

A_mobile A_stationary
The equilibrium constant, K, is termed the partition coefficient; defined as the molar concentration of analyte in the stationary phase divided by the molar concentration of the analyte in the mobile phase.
The time between sample injection and an analyte peak reaching a detector at the end of the column is termed the retention time (tR ). Each analyte in a sample will have a different retention time. The time taken for the mobile phase to pass through the column is called tM.
A term called the retention factor, k', is often used to describe the migration rate of an analyte on a column. You may also find it called the capacity factor. The retention factor for analyte A is defined as;

k'A = t R - tM / tM
t R and tM are easily obtained from a chromatogram. When an analytes retention factor is less than one, elution is so fast that accurate determination of the retention time is very difficult. High retention factors (greater than 20) mean that elution takes a very long time. Ideally, the retention factor for an analyte is between one and five.
We define a quantity called the selectivity factor, a , which describes the separation of two species (A and B) on the column;

a = k 'B / k 'A
When calculating the selectivity factor, species A elutes faster than species B. The selectivity factor is always greater than one.

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Band broadening and column efficiency

To obtain optimal separations, sharp, symmetrical chromatographic peaks must be obtained. This means that band broadening must be limited. It is also beneficial to measure the efficiency of the column.

The Theoretical Plate Model of Chromatography
The plate model supposes that the chromatographic column is contains a large number of separate layers, called theoretical plates. Separate equilibrations of the sample between the stationary and mobile phase occur in these "plates". The analyte moves down the column by transfer of equilibrated mobile phase from one plate to the next.
It is important to remember that the plates do not really exist; they are a figment of the imagination that helps us understand the processes at work in the column.They also serve as a way of measuring column efficiency, either by stating the number of theoretical plates in a column, N (the more plates the better), or by stating the plate height; the Height Equivalent to a Theoretical Plate (the smaller the better).
If the length of the column is L, then the HETP is

HETP = L / N
The number of theoretical plates that a real column possesses can be found by examining a chromatographic peak after elution;


where w_1/2 is the peak width at half-height.
As can be seen from this equation, columns behave as if they have different numbers of plates for different solutes in a mixture.

The Rate Theory of Chromatography
A more realistic description of the processes at work inside a column takes account of the time taken for the solute to equilibrate between the stationary and mobile phase (unlike the plate model, which assumes that equilibration is infinitely fast). The resulting band shape of a chromatographic peak is therefore affected by the rate of elution. It is also affected by the different paths available to solute molecules as they travel between particles of stationary phase. If we consider the various mechanisms which contribute to band broadening, we arrive at the Van Deemter equation for plate height;

HETP = A + B / u + C u
where u is the average velocity of the mobile phase. A, B, and C are factors which contribute to band broadening.
A - Eddy diffusion
The mobile phase moves through the column which is packed with stationary phase. Solute molecules will take different paths through the stationary phase at random. This will cause broadening of the solute band, because different paths are of different lengths.
B - Longitudinal diffusion
The concentration of analyte is less at the edges of the band than at the center. Analyte diffuses out from the center to the edges. This causes band broadening. If the velocity of the mobile phase is high then the analyte spends less time on the column, which decreases the effects of longitudinal diffusion.
C - Resistance to mass transfer
The analyte takes a certain amount of time to equilibrate between the stationary and mobile phase. If the velocity of the mobile phase is high, and the analyte has a strong affinity for the stationary phase, then the analyte in the mobile phase will move ahead of the analyte in the stationary phase. The band of analyte is broadened. The higher the velocity of mobile phase, the worse the broadening becomes.
Van Deemter plots
A plot of plate height vs. average linear velocity of mobile phase.

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Such plots are of considerable use in determining the optimum mobile phase flow rate.

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Resolution

Although the selectivity factor, a, describes the separation of band centres, it does not take into account peak widths. Another measure of how well species have been separated is provided by measurement of the resolution. The resolution of two species, A and B, is defined as
Baseline resolution is achieved when R = 1.5
It is useful to relate the resolution to the number of plates in the column, the selectivity factor and the retention factors of the two solutes;
To obtain high resolution, the three terms must be maximised. An increase in N, the number of theoretical plates, by lengthening the column leads to an increase in retention time and increased band broadening - which may not be desirable. Instead, to increase the number of plates, the height equivalent to a theoretical plate can be reduced by reducing the size of the stationary phase particles.
It is often found that by controlling the capacity factor, k', separations can be greatly improved. This can be achieved by changing the temperature (in Gas Chromatography) or the composition of the mobile phase (in Liquid Chromatography).
The selectivity factor, a, can also be manipulated to improve separations. When a is close to unity, optimising k' and increasing N is not sufficient to give good separation in a reasonable time. In these cases,k' is optimised first, and then a is increased by one of the following procedures:

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1. Changing mobile phase composition
2. Changing column temperature
3. Changing composition of stationary phase
4. Using special chemical effects (such as incorporating a species which complexes with one of the solutes into the stationary phase)

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BEERS LAW

Introduction

Many compounds absorb ultraviolet (UV) or visible (Vis.) light. The diagram below shows a beam of monochromatic radiation of radiant power P₀, directed at a sample solution. Absorption takes place and the beam of radiation leaving the sample has radiant power P.

The amount of radiation absorbed may be measured in a number of ways: Transmittance, T = P / P0% Transmittance, %T = 100 T Absorbance, A = log10 P0 / PA = log10 1 / T  A = log10 100 / %T A = 2 - log10 %T

The last equation, A = 2 - log₁₀ %T , is worth remembering because it allows you to easily calculate absorbance from percentage transmittance data.

The relationship between absorbance and transmittance is illustrated in the following diagram:

So, if all the light passes through a solution without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero, and absorption is infinite.

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The Beer-Lambert Law

Now let us look at the Beer-Lambert law and explore it's significance. This is important because people who use the law often don't understand it - even though the equation representing the law is so straightforward:

A=ebc

Where A is absorbance (no units, since A = log₁₀ P₀ / P )
e is the molar absorbtivity with units of L mol^-1 cm^{-1
b is the path length of the sample - that is, the path length of the cuvette in which the sample is contained. We will express this measurement in centimetres.
c is the concentration of the compound in solution, expressed in mol L-1}

The reason why we prefer to express the law with this equation is because absorbance is directly proportional to the other parameters, as long as the law is obeyed. We are not going to deal with deviations from the law.

Let's have a look at a few questions...

Question : Why do we prefer to express the Beer-Lambert law using absorbance as a measure of the absorption rather than %T ?

Answer : To begin, let's think about the equations...

A=ebc

%T = 100 P/P₀ = e ^-ebc

Now, suppose we have a solution of copper sulphate (which appears blue because it has an absorption maximum at 600 nm). We look at the way in which the intensity of the light (radiant power) changes as it passes through the solution in a 1 cm cuvette. We will look at the reduction every 0.2 cm as shown in the diagram below. The Law says that the fraction of the light absorbed by each layer of solution is the same. For our illustration, we will suppose that this fraction is 0.5 for each 0.2 cm "layer" and calculate the following data:

Path length / cm	0	0.2	0.4	0.6	0.8	1.0
%T	100	50	25	12.5	6.25	3.125
Absorbance	0	0.3	0.6	0.9	1.2	1.5

A = ebc tells us that absorbance depends on the total quantity of the absorbing compound in the light path through the cuvette. If we plot absorbance against concentration, we get a straight line passing through the origin (0,0).

Note that the Law is not obeyed at high concentrations. This deviation from the Law is not dealt with here.

The linear relationship between concentration and absorbance is both simple and straightforward, which is why we prefer to express the Beer-Lambert law using absorbance as a measure of the absorption rather than %T.

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Question : What is the significance of the molar absorbtivity, e ?

Answer : To begin we will rearrange the equation A = ebc :

e = A / bc

In words, this relationship can be stated as "e is a measure of the amount of light absorbed per unit concentration".

Molar absorbtivity is a constant for a particular substance, so if the concentration of the solution is halved so is the absorbance, which is exactly what you would expect.

Let us take a compound with a very high value of molar absorbtivity, say 100,000 L mol^-1 cm^-1, which is in a solution in a 1 cm pathlength cuvette and gives an absorbance of 1.

e = 1 / 1 ´ c

Therefore, c = 1 / 100,000 = 1 ´ 10^-5 mol L^-1

Now let us take a compound with a very low value of e, say 20 L mol^-1 cm^-1 which is in solution in a 1 cm pathlength cuvette and gives an absorbance of 1.

e = 1 / 1 ´ c

Therefore, c = 1 / 20 = 0.05 mol L^-1

The answer is now obvious - a compound with a high molar absorbtivity is very effective at absorbing light (of the appropriate wavelength), and hence low concentrations of a compound with a high molar absorbtivity can be easily detected.

Question : What is the molar absorbtivity of Cu²⁺ ions in an aqueous solution of CuSO₄ ? It is either 20 or 100,000 L mol^-1 cm^-1

Answer : I am guessing that you think the higher value is correct, because copper sulphate solutions you have seen are usually a beautiful bright blue colour. However, the actual molar absorbtivity value is 20 L mol^-1 cm^-1 ! The bright blue colour is seen because the concentration of the solution is very high.

b-carotene is an organic compound found in vegatables and is responsible for the colour of carrots. It is found at exceedingly low concentrations. You may not be surprised to learn that the molar absorbtivity of b-carotene is 100,000 L mol^-1 cm^-1 !

GAS CHROMATOGRAPHY

Introduction

Gas chromatography - specifically gas-liquid chromatography - involves a sample being vapourised and injected onto the head of the chromatographic column. The sample is transported through the column by the flow of inert, gaseous mobile phase. The column itself contains a liquid stationary phase which is adsorbed onto the surface of an inert solid.
Have a look at this schematic diagram of a gas chromatograph:

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Instrumental components

Carrier gas

The carrier gas must be chemically inert. Commonly used gases include nitrogen, helium, argon, and carbon dioxide. The choice of carrier gas is often dependant upon the type of detector which is used. The carrier gas system also contains a molecular sieve to remove water and other impurities.

Sample injection port

For optimum column efficiency, the sample should not be too large, and should be introduced onto the column as a "plug" of vapour - slow injection of large samples causes band broadening and loss of resolution. The most common injection method is where a microsyringe is used to inject sample through a rubber septum into a flash vapouriser port at the head of the column. The temperature of the sample port is usually about 50°C higher than the boiling point of the least volatile component of the sample. For packed columns, sample size ranges from tenths of a microliter up to 20 microliters. Capillary columns, on the other hand, need much less sample, typically around 10^-3 mL. For capillary GC, split/splitless injection is used. Have a look at this diagram of a split/splitless injector;

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The injector can be used in one of two modes; split or splitless. The injector contains a heated chamber containing a glass liner into which the sample is injected through the septum. The carrier gas enters the chamber and can leave by three routes (when the injector is in split mode). The sample vapourises to form a mixture of carrier gas, vapourised solvent and vapourised solutes. A proportion of this mixture passes onto the column, but most exits through the split outlet. The septum purge outlet prevents septum bleed components from entering the column.

Columns
There are two general types of column, packed and capillary (also known as open tubular). Packed columns contain a finely divided, inert, solid support material (commonly based on diatomaceous earth) coated with liquid stationary phase. Most packed columns are 1.5 - 10m in length and have an internal diameter of 2 - 4mm.
Capillary columns have an internal diameter of a few tenths of a millimeter. They can be one of two types; wall-coated open tubular (WCOT) or support-coated open tubular (SCOT). Wall-coated columns consist of a capillary tube whose walls are coated with liquid stationary phase. In support-coated columns, the inner wall of the capillary is lined with a thin layer of support material such as diatomaceous earth, onto which the stationary phase has been adsorbed. SCOT columns are generally less efficient than WCOT columns. Both types of capillary column are more efficient than packed columns.
In 1979, a new type of WCOT column was devised - the Fused Silica Open Tubular (FSOT) column;
These have much thinner walls than the glass capillary columns, and are given strength by the polyimide coating. These columns are flexible and can be wound into coils. They have the advantages of physical strength, flexibility and low reactivity.

Column temperature
For precise work, column temperature must be controlled to within tenths of a degree. The optimum column temperature is dependant upon the boiling point of the sample. As a rule of thumb, a temperature slightly above the average boiling point of the sample results in an elution time of 2 - 30 minutes. Minimal temperatures give good resolution, but increase elution times. If a sample has a wide boiling range, then temperature programming can be useful. The column temperature is increased (either continuously or in steps) as separation proceeds.

Detectors
There are many detectors which can be used in gas chromatography. Different detectors will give different types of selectivity. A non-selective detector responds to all compounds except the carrier gas, aselective detector responds to a range of compounds with a common physical or chemical property and a specific detector responds to a single chemical compound. Detectors can also be grouped intoconcentration dependant detectors and mass flow dependant detectors. The signal from a concentration dependant detector is related to the concentration of solute in the detector, and does not usually destroy the sample Dilution of with make-up gas will lower the detectors response. Mass flow dependant detectors usually destroy the sample, and the signal is related to the rate at which solute molecules enter the detector. The response of a mass flow dependant detector is unaffected by make-up gas. Have a look at this tabular summary of common GC detectors:

Detector	Type	Support gases	Selectivity	Detectability	Dynamic range
Flame ionization (FID)	Mass flow	Hydrogen and air	Most organic cpds.	100 pg	107
Thermal conductivity (TCD)	Concentration	Reference	Universal	1 ng	107
Electron capture (ECD)	Concentration	Make-up	Halides, nitrates, nitriles, peroxides, anhydrides, organometallics	50 fg	105
Nitrogen-phosphorus	Mass flow	Hydrogen and air	Nitrogen, phosphorus	10 pg	106
Flame photometric (FPD)	Mass flow	Hydrogen and air possibly oxygen	Sulphur, phosphorus, tin, boron, arsenic, germanium, selenium, chromium	100 pg	103
Photo-ionization (PID)	Concentration	Make-up	Aliphatics, aromatics, ketones, esters, aldehydes, amines, heterocyclics, organosulphurs, some organometallics	2 pg	107
Hall electrolytic conductivity	Mass flow	Hydrogen, oxygen	Halide, nitrogen, nitrosamine, sulphur

The effluent from the column is mixed with hydrogen and air, and ignited. Organic compounds burning in the flame produce ions and electrons which can conduct electricity through the flame. A large electrical potential is applied at the burner tip, and a collector electrode is located above the flame. The current resulting from the pyrolysis of any organic compounds is measured. FIDs are mass sensitive rather than concentration sensitive; this gives the advantage that changes in mobile phase flow rate do not affect the detector's response. The FID is a useful general detector for the analysis of organic compounds; it has high sensitivity, a large linear response range, and low noise. It is also robust and easy to use, but unfortunately, it destroys the sample.

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