Spectroscopy Absorption | Emission | Scattering
Introduction Spectroscopy is the use of the absorption, emission, or scattering of electromagnetic radiation by atoms or molecules (or atomic or molecular ions) to qualitatively or quantitatively study the atoms or molecules, or to study physical processes. The interaction of radiation with matter can cause redirection of the radiation and/or transitions between the energy levels of the atoms or molecules. A transition from a lower level to a higher level with transfer of energy from the radiation field to the atom or molecule is called absorption. A transition from a higher level to a lower level is called emission if energy is transfered to the radiation field, or nonradiative decay if no radiation is emitted. Redirection of light due to its interaction with matter is called scattering, and may or may not occur with transfer of energy, i.e., the scattered radiation has a slightly different or the same wavelength.
Absorption When atoms or molecules absorb light, the incoming energy excites a quantized structure to a higher energy level. The type of excitation depends on the wavelength of the light. Electrons are promoted to higher orbitals by ultraviolet or visible light, vibrations are excited by infrared light, and rotations are excited by microwaves. An absorption spectrum is the absorption of light as a function of wavelength. The spectrum of an atom or molecule depends on its energy level structure, and absorption spectra are useful for identifying of compounds. Measuring the concentration of an absorbing species in a sample is accomplished by applying the Beer-Lambert Law.
Emission Atoms or molecules that are excited to high energy levels can decay to lower levels by emitting radiation (emission or luminescence). For atoms excited by a high-temperature energy source this light emission is commonly called atomic or optical emission (see atomic-emission spectroscopy), and for atoms excited with light it is called atomic fluorescence (see atomic-fluorescence spectroscopy). For molecules it is called fluorescence if the transition is between states of the same spin and phosphorescence if the transition occurs between states of different spin.
The emission intensity of an emitting substance is linearly proportional to analyte concentration at low concentrations, and is useful for quantitating emitting species.
Scattering When electromagnetic radiation passes through matter, most of the radiation continues in its original direction but a small fraction is scattered in other directions. Light that is scattered at the same wavelength as the incoming light is called Rayleigh scattering. Light that is scattered in transparent solids due to vibrations (phonons) is called Brillouin scattering. Brillouin scattering is typically shifted by 0.1 to 1 cm-1 from the incident light. Light that is scattered due to vibrations in molecules or optical phonons in solids is called Raman scattering. Raman scattered light is shifted by as much as 4000 cm-1 from the incident light.
Electromagnetic Radiation Introduction Electromagnetic radiation is an energy wave that is composed of an electric field component and a magnetic field component. The electric and magnetic fields are orthogonal to each other and orthogonal to the direction of propogation of the wave. Schematic of an electromagnetic wave
The wavelength is the length of one complete oscillation and the frequency is the number of oscillations per second. Electromagnetic waves travel through a vacuum at 2.99792x108 m/s, which is known as the speed of light. The relation between speed of light (c), wavelength (lambda), and frequency (nu) is: c = lambda * nu
Wave-particle duality
Electromagnetic radiation shows both wave and particle characteristics depending on how the radiation is observed. Einstein first postulated that the energy of radiation is quantized and that radiation is composed of energy packets that were later named photons. The energy (E) of a photon depends on its frequency (or wavelength): E = h * nu = h * c / lambda where h is Planck's constant (6.62618x10-34 Js), nu is the frequency of the radiation (Hz), c is the speed of light (2.99792x108 m/s), and lambda is wavelength (m).
de Broglie equation Analogous to radiation, particles; such as electrons, protons, and neutrons have wave properties as determined by the de Broglie equation: lambda = h/p where lambda is wavelength, h is Planck's constant, and p is the momentum of the particle.
Beer-Lambert Law Introduction The Beer-Lambert law (or Beer's law) is the linear relationship between absorbance and concentration of an absorbing species. The general Beer-Lambert law is usually written as: A = a(lambda) * b * c where A is the measured absorbance, a(lambda) is a wavelength-dependent absorptivity coefficient, b is the path length, and c is the analyte concentration. When working in concentration units of molarity, the Beer-Lambert law is written as: A = epsilon * b * c where epsilon is the wavelength-dependent molar absorptivity coefficient with units of M-1 cm-1.
Instrumentation Experimental measurements are usually made in terms of transmittance (T), which is defined as: T = I / Io where I is the light intensity after it passes through the sample and Io is the initial light intensity. The relation between A and T is: A = -log T = - log (I / Io).
Absorption of light by a sample
Modern absorption instruments can usually display the data as either transmittance, %transmittance, or absorbance. An unknown concentration of an analyte can be determined by measuring the amount of light that a sample absorbs and applying Beer's law. If the absorptivity coefficient is not known, the unknown concentration can be determined using a working curve of absorbance versus concentration derived from standards.
Derivation of the Beer-Lambert law The Beer-Lambert law can be derived from an approximation for the absorption coefficient for a molecule by approximating the molecule by an opaque disk whose crosssectional area, sigma, represents the effective area seen by a photon of frequency w. If the frequency of the light is far from resonance, the area is approximately 0, and if w is close to resonance the area is a maximum. Taking an infinitesimal slab, dz, of sample:
Io is the intensity entering the sample at z=0, Iz is the intensity entering the infinitesimal slab at z, dI is the intensity absorbed in the slab, and I is the intensity of light leaving the sample. Then, the total opaque area on the slab due to the absorbers is sigma * N * A * dz. Then, the fraction of photons absorbed will be sigma * N * A * dz / A so, dI / Iz = - sigma * N * dz
Integrating this equation from z = 0 to z = b gives: ln(I) - ln(Io) = - sigma * N * b or - ln(I / Io) = sigma * N * b. Since N (molecules/cm3) * (1 mole / 6.023x1023 molecules) * 1000 cm3 / liter = c (moles/liter) and 2.303 * log(x) = ln(x) then - log(I / Io) = sigma * (6.023x1020 / 2.303) * c * b or - log(I / Io) = A = epsilon * b * c where epsilon = sigma * (6.023x1020 / 2.303) = sigma * 2.61x1020 Typical cross-sections and molar absorptivities are: epsilon (M-1 cm-1) absorption - atoms molecules infrared Raman scattering
sigma (cm2) 10-12 10-16 10-19 10-29
3x108 3x104 3x10 3x10-9
Limitations of the Beer-Lambert law The linearity of the Beer-Lambert law is limited by chemical and instrumental factors. Causes of nonlinearity include: • • • • • • •
deviations in absorptivity coefficients at high concentrations (>0.01M) due to electrostatic interactions between molecules in close proximity scattering of light due to particulates in the sample fluoresecence or phosphorescence of the sample changes in refractive index at high analyte concentration shifts in chemical equilibria as a function of concentration non-monochromatic radiation, deviations can be minimized by using a relatively flat part of the absorption spectrum such as the maximum of an absorption band stray light
Quantitative Fluorimetry
Introduction Light emission from atoms or molecules can be used to quantitate the amount of the emitting substance in a sample. The relationship between fluorescence intensity and analyte concentration is: F = k * QE * Po * (1-10[-epsilon*b*c]) where F is the measured fluorescence intensity, k is a geometric instrumental factor, QE is the quantum efficiency (photons emitted/photons absorbed), Po is the radiant power of the excitation source, epsilon is the wavelength-dependent molar absorptivity coefficient, b is the path length, and c is the analyte concentration (epsilon, b, and c are the same as used in the Beer-Lambert law). Expanding the above equation in a series and dropping higher terms gives: F = k * QE * Po * (2.303 * epsilon * b * c) This relationship is valid at low concentrations (<10-5 M) and shows that fluorescence intensity is linearly proportional to analyte concentration. Determining unknown concentrations from the amount of fluorescence that a sample emits requires calibration of a fluorimeter with a standard (to determine K and QE) or by using a working curve.
Limitations Many of the limitations of the Beer-Lambert law also affect quantitative fluorimetry. Fluorescence measurements are also susceptible to inner-filter effects. These effects include excessive absorption of the excitation radiation (pre-filter effect) and selfabsorption of atomic resonance fluorescence (post-filter effect).
Specific fluorescence techniques • •
Atomic fluorescence spectroscopy (AFS) Molecular laser-induced fluorescence (LIF)
Laser-Induced Fluorescence (LIF) Introduction Laser-induced fluorescence (LIF) is the optical emission from molecules that have been excited to higher energy levels by absorption of electromagnetic radiation. The main advantage of fluorescence detection compared to absorption measurements is the greater sensitivity achievable because the fluorescence signal has a very low background. For molecules that can be resonant excitated, LIF provides selective excitation of the analyte
to avoid interferences. LIF is useful to study the electronic structure of molecules and to make quantitative measurements of analyte concentrations. Analytical applications include monitoring gas-phase concentrations in the atmosphere, flames, and plasmas; and remote sensing using light detection and ranging (LIDAR). Because of the differences in the nature of the energy-level structure between atoms and molecules, the discussion on atomic fluorescence spectroscopy is in a separate document.
Instrumentation The excitation source for molecular LIF is typically a tunable dye laser in the visible spectral region. Studies in the near-ultraviolet and near-infrared are becoming more common as near-infrared lasers and frequency-doubling methods improve. Highresolution studies require cooling of the molecules to remove spectral congestion and to reduce the Doppler width of the transitions. A separate document on high-resolution spectroscopy describes cooling methods such as molecular beams, free-jet expansions, and cryogenic glass or crystalline matrices.
Atomic Transitions - Theory Introduction The probability that an atomic spectroscopic transition will occur is called the transition probability or transition strength. This probability will determine the extent to which an atom will absorb light at a resonance frequency, and the intensity of the emission lines from an atomic excited state. The spectral width of a spectroscopic transition depends on the widths of the initial and final states. The width of the ground state is essentially a delta function and the width of an excited state depends on its lifetime.
Specific Documents • • •
Transition strengths Excited-state lifetime and the natural linewidth Transition lineshapes and broadening
Spectroscopic Transition Strengths Introduction An atom or molecule can be stimulated by light to change from one energy state to another. An atom or molecule in an excited energy state can also decay spontaneously to a lower state. The probability of an atom or molecule changing states depends on the
nature of the initial and final state wavefunctions, how strongly light can interact with them, and on the intensity of any incident light. This document discusses some of the practical terms used to describe the probability of a transition occuring, which is commonly called the transition strength. To a first approximation, transitions strengths are governed by selection rules which determine whether a transition is allowed or disallowed. Practical measurements of transitions strengths are usually described in terms of the Einstein A and B coefficients or the oscillator strength (f).
Selection Rules 1. The parity of the initial and final wavefunctions must be different. 2. The spin can not change, deltaS = 0. 3. The change in orbital angular momentum can be deltaL = 0, ±1, but L=0 to L=0 transitions are not allowed. 4. The change in total angular momentum can be deltaJ = 0, ±1, but J=0 to J=0 transitions are not allowed.
Transition Probability The transition probability is R2 with units of J cm3, where R is the transition moment given by: R=<X|u|X> and u is the dipole moment operator. Basically what this equation indicates is that the strength of a transition is relative to how strongly the dipole moment of a resonance between energy states can couple to the electric field of a light wave.
Einstein coefficients For a two-level system (ground-state level i and upper level j), the rate of an upward stimulated transition (absorption, -dNi/dt or dNj/dt) is:
where Ni is the number density of atoms in the ground state, Uv is the light intensity, and the proportionality factor Bij is the Einstein B coefficient for absorption:
For stimulated emission the Einstein coefficient becomes:
where gi and gj are the degeneracies of the ground and excited states, respectively.
Atoms in the excited state can decay without the presence of an external light field due to stimulation due to "zero-point fluctuations." Zero-point fluctuations are the dynamic variations in the shape of an electronic orbital at any instant in time. These instantaneous orbitals can be described by a linear combination of the wavefunctions of the system, which provides the mechanism for transitions between different states of the system. The spontaneous decay rate (-dNj/dt or dNi/dt) is: -dNj/dt = Nj * Aji where Aji is the Einstein coefficient for spontaneous emission:
Since atoms in the upper level can decay by both spontaneous and stimulated emission, the total downward rate (-dNj/dt or dNi/dt) is given by:
Oscillator strength The oscillator strength of a transition is a dimensionless number that is useful for comparing different transitions. It is defined as the ratio of the strength an atomic or molecular transition to the theoretical transition strength of a single electron using a harmonic-oscillator model. For absorption:
and for emission: fji = fij gi/gj
Oscillator strengths can range from 0 to 1, or a small integer. A strong transition will have an f close to 1. Oscillator strengths greater than 1 result from the degeneracy of real electronic systems. Tabulations in the literature often use gf, where gf = gi fij = gj fji
Atomic-Absorption Spectroscopy (AA) Introduction Atomic-absorption (AA) spectroscopy uses the absorption of light to measure the concentration of gas-phase atoms. Since samples are usually liquids or solids, the analyte atoms or ions must be vaporized in a flame or graphite furnace. The atoms absorb
ultraviolet or visible light and make transitions to higher electronic energy levels. The analyte concentration is determined from the amount of absorption. Applying the BeerLambert law directly in AA spectroscopy is difficult due to variations in the atomization efficiency from the sample matrix, and nonuniformity of concentration and path length of analyte atoms (in graphite furnace AA). Concentration measurements are usually determined from a working curve after calibrating the instrument with standards of known concentration. Schematic of an atomic-absorption experiment
Instrumentation
Light source The light source is usually a hollow-cathode lamp of the element that is being measured. Lasers are also used in research instruments. Since lasers are intense enough to excite atoms to higher energy levels, they allow AA and atomic fluorescence measurements in a single instrument. The disadvantage of these narrow-band light sources is that only one element is measurable at a time.
Atomizer AA spectroscopy requires that the analyte atoms be in the gas phase. Ions or atoms in a sample must undergo desolvation and vaporization in a high-temperature source such as a flame or graphite furnace. Flame AA can only analyze solutions, while graphite furnace AA can accept solutions, slurries, or solid samples. Flame AA uses a slot type burner to increase the path length, and therefore to increase the total absorbance (see Beer-Lambert law). Sample solutions are usually aspirated with the gas flow into a nebulizing/mixing chamber to form small droplets before entering the flame. The graphite furnace has several advantages over a flame. It is a much more efficient atomizer than a flame and it can directly accept very small absolute quantities of sample. It also provides a reducing environment for easily oxidized elements. Samples are placed directly in the graphite furnace and the furnace is electrically heated in several steps to dry the sample, ash organic matter, and vaporize the analyte atoms.
Light separation and detection AA spectrometers use monochromators and detectors for uv and visible light. The main purpose of the monochromator is to isolate the absorption line from background light due to interferences. Simple dedicated AA instruments often replace the monochromator with a bandpass interference filter. Photomultiplier tubes are the most common detectors for AA spectroscopy. Picture of a flame atomic-absorption spectrometer:
Picture of a graphite-furnace atomic-absorption spectrometer:
Atomic Emission Spectroscopy (AES, OES) Introduction Atomic emission spectroscopy (AES or OES) uses quantitative measurement of the optical emission from excited atoms to determine analyte concentration. Analyte atoms in solution are aspirated into the excitation region where they are desolvated, vaporized, and atomized by a flame, discharge, or plasma. These high-temperature atomization sources provide sufficient energy to promote the atoms into high energy levels. The atoms decay back to lower levels by emitting light. Since the transitions are between distinct atomic energy levels, the emission lines in the spectra are narrow. The spectra of multi-elemental samples can be very congested, and spectral separation of nearby atomic transitions requires a high-resolution spectrometer. Since all atoms in a sample are excited simultaneously, they can be detected simultaneously, and is the major advantage of AES compared to atomic-absorption (AA) spectroscopy. Schematic of an AES experiment
Instrumentation As in AA spectroscopy, the sample must be converted to free atoms, usually in a hightemperature excitation source. Liquid samples are nebulized and carried into the excitation source by a flowing gas. Solid samples can be introduced into the source by a slurry or by laser ablation of the solid sample in a gas stream. Solids can also be directly vaporized and excited by a spark between electrodes or by a laser pulse. The excitation source must desolvate, atomize, and excite the analyte atoms. A variety of excitation sources are described in separate documents: • • • • •
Direct-current plasma (DCP) Flame Inductively-coupled plasma (ICP) Laser-induced breakdown (LIBS) Laser-induced plasma
• •
Microwave-induced plasma (MIP) Spark or arc
Since the atomic emission lines are very narrow, a high-resolution polychromator is needed to selectively monitor each emission line. Picture of an inductively-coupled plasma atomic emission spectrometer
Direct-Current Plasma Excitation Source Introduction A direct-current plasma (DCP) is created by an electrical discharge between two electrodes. A plasma support gas is necessary, and Ar is common. Samples can be deposited on one of the electrodes, or if conducting can make up one electrode. Insulating solid samples are placed near the discharge so that ionized gas atoms sputter the sample into the gas phase where the analyte atoms are excited. This sputtering process is often referred to as glow-discharge excitation.
Flame Excitation Source Introduction
A flame provides a high-temperature source for desolvating and vaporizing a sample to obtain free atoms for spectroscopic analysis. In atomic absorption spectroscopy ground state atoms are desired. For atomic emission spectroscopy the flame must also excite the atoms to higher energy levels. The table lists temperatures that can be achieved in some commonly used flames. Temperatures of some common flames Fuel Oxidant Temperature (K) H2 Air 2000-2100 C2H2 Air 2100-2400 H2 O2 2600-2700 C2H2 N2O 2600-2800
Introduction The figure shows a total consumption burner in which the sample solution is directly aspirated into the flame. This flame design is common for atomic emission spectroscopy. All desolvation, atomization, and excitation occurs in the flame. Other flame designs nebulize the sample and premix it with the fuel and oxidant before it reaches the burner. Atomic-absorption instruments almost always use a nebulizer and also use slot burner to increase the path length for the sample absorption.
a
Inductively-Coupled Plasma (ICP) Excitation Source Introduction An inductively coupled plasma (ICP) is a very high temperture (7000-8000K) excitation source that efficiently desolvates, vaporizes, excites, and ionizes atoms. Molecular interferences are greatly reduced with this excitation source but are not eliminated completely. ICP sources are used to excite atoms for atomic-emission spectroscopy and to ionize atoms for mass spectrometry.
Instrumentation The sample is nebulized and entrained in the flow of plasma support gas, which is typically Ar. The plasma torch consists of concentric quartz tubes. The inner tube contains the sample aerosol and Ar support gas and the outer tube contains flowing gas to keep the tubes cool. A radiofrequency (RF) generator (typically 1-5 kW @ 27 MHz) produces an oscillating current in an induction coil that wraps around the tubes. The induction coil creates an oscillating magnetic field, which produces an oscillating magnetic field The magnetic field in turn sets up an oscillating current in the ions and electrons of the support gas (argon). As the ions and electrons collide with other atoms in the support gas
Laser-Induced Breakdown Excitation Source Introduction When a high-energy laser pulse is focused into a gas or liquid, or onto a solid surface, it can cause dielectric breakdown and create a hot plasma. For solids the laser pulse also ablates material into the gas phase. The energy of the laser-created plasma can atomize, excite, and ionize analyte species, which can then be detected and quantified by atomicemission spectroscopy or mass spectrometry.
Laser-Induced Plasma Excitation Source Introduction A high-power CO2 laser that is focused into a support gas, such as Ar, can maintain a hot plasma. The energy of the plasma can atomize, excite, and ionize analyte species present in the support gas, which can then be detected and quantified by atomic-emission
spectroscopy or mass spectrometry. It can also be used in a glow-discharge mode to sputter analyte atoms off of a solid surface for analysis in the plasma.
Microwave-Induced Plasma Excitation Source Introduction A microwave-induced plama consists of a quartz tube surrounded by a microwave waveguide or cavity. Microwaves produced from a magnetron (a microwave generator) fill the waveguide or cavity and cause the electrons in the plasma support gas to oscillate. The oscillating electons collide with other atoms in the flowing gas to create and maintain a high-temperature plasma. As in inductively coupled plasmas, a spark is needed to create some initial electrons to create the plasma. Atomic emission is measured from excited analyte atoms as they exit the microwave waveguide or cavity.
Spark and Arc Emission Sources Introduction Spark and arc excitation sources use a current pulse (spark) or a continuous electical discharge (arc) between two electrodes to vaporize and excite analyte atoms. The electrodes are either metal or graphite. If the sample to be analyzed is a metal, it can be used as one electrode. Non-conducting samples are ground with graphite powder and placed into a cup-shaped lower electrode. Arc and spark sources can be used to excite atoms for atomic-emission spectroscopy or to ionize atoms for mass spectrometry. Arc and spark excitation sources have been replaced in many applications with plasma or laser sources, but are still widely used in the metals industry.
Atomic-Fluorescence Spectroscopy (AFS)
Introduction Atomic fluorescence is the optical emission from gas-phase atoms that have been excited to higher energy levels by absorption of electromagnetic radiation. The main advantage of fluorescence detection compared to absorption measurements is the greater sensitivity achievable because the fluorescence signal has a very low background. The resonant excitation provides selective excitation of the analyte to avoid interferences. AFS is useful to study the electronic structure of atoms and to make quantitative measurements. Analytical applications include flames and plasmas diagnostics, and enhanced sensitivity in atomic analysis. Because of the differences in the nature of the energy-level structure between atoms and molecules, discussion of laser-induced fluorescence (LIF) from molecules is found in a separate document.
Instrumentation Analysis of solutions or solids requires that the analyte atoms be desolvated, vaporized, and atomized at a relatively low temperature in a heat pipe, flame, or graphite furnace. A hollow-cathode lamp or laser provides the resonant excitation to promote the atoms to higher energy levels. The atomic fluorescence is dispersed and detected by monochromators and photomultiplier tubes, similar to atomic-emission spectroscopy instrumentation.
Electron Paramagnetic Resonance (EPR, ESR) Spectroscopy Introduction When an atom or molecule with an unpaired electron is placed in a magnetic field, the spin of the unpaired electron can align either in the same direction or in the opposite direction as the field. These two electron alignments have different energies and application of a magnetic field to an unpaired electron lifts the degeneracy of the ±1/2 spins of the electron. Electron-paramagnetic-resonance (EPR) or electron-spin-resonance (ESR) spectroscopy measures the