Instrumental Analysis Test II

Wave Nature of Electromagnetic Radiation

Consists of perpendicular, oscillating electric and magnetic fields; fields oscillate 90 degrees to the direction of wave propagation


Electric field considered since interacts with matter and is responsible for reflection, transmission, refraction, and absorption of radiation.

Wave Period

Time required for successive maxima to pass through a fixed point in space

 

Time required to complete one full oscillation

Wave Frequency
The number of oscillations of the field that ocur per second. Equal to 1/p. Frequency is set by the source and is unchanged by the medium through which the radiation travels.
Wave Velocity of Propagation
The rate at which the wave front moves through a medium; depends on the composition of the medium and the frequency
Wavelength
The linear distance between successive maxima or minima of the wave
Wave Amplitude
The height of a wave at its maxima
Relationship between velocity, wavelength, and frequency

V = νλ

In a vacuum, velocity is independent of frequency;

c = 3×1010 cm/sec

In any other medium, its velocity is slower because the socillating electric field interacts with the electrons in the medium.  If the frequency is to be unchanged and velocity decreases for a change in mdium, then the wavelength must also decrease in the medium.

Wavenumber
Number of waves per centimeter; equal to 1/λ
Wave Power
The energy of a beam reaching a given area per second
Wave Intensity
The power per unit solid angle
Diffraction

Process in which a parallel beam of radiation is bent as it passes through a narrow opening.


If the opening width, d, is wide relative to the wavelength of the motion, there is no detectable diffraction.  If the opening is small compared to the wavelength, diffraction is detected.

Young Double-Slit Experiment

 

(Interference)

Parallel, monochromatic beam of radiation passes through a single slit producing a coherent beam of radtion which impinges upon two closely spaced slits.  Radiation emerging from these slits produces an alternating light-dark series of images.  Intensities of the bands decrease in intensity from the central band.


Constructive Interference:

nλ = dsinΘ


Destructive Interference:

nλ/2 = dsinΘ

Transmission

The fraction of radiated energy that is transferred through a medium

Oscillating electric field of the radiation causes the bound electrons of the particles in the medium to oscillate. 
Oscillation results in a polarization of the particles. 
If the radiation is not absorbed, the energy of polarization is retained momentarily (10-15 sec) and reemitted without alteration as the particle returns to its original state. 
Velocity has been slowed by the time for retention and reemission. 
If the particles of the medium are small destructive interference prevents propagation in any direction other than the original light path. 
If particle size is large such as in polymers of colloids scattering results.

Refraction

Change in direction of a light beam as a consequence of differences in its velocity in two media.


Beam is bent toward the normal in the denser (slower) medium

Snell’s Law

sin;1/sin;2 = n1/n2 = V1/V2

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Describes refraction

Reflection

Change in direction of a beam of radiation as a result of crossing an interface between media with differing refractive indexes.

Fraction of reflected radiation increases with increasing differences between refractive indexes.

Process reduces the intensity of the transmitted beam.

Particle Model of Electromagnetic Radiation
When electromagnetic radiation is absorbed or emitted, a permanent transfer of energy to the absorbing medium from the emitting medium occurs; this interaction can be described by thinking of electromagnetic radiation as discrete particles called photons or quanta.
Photoelectric Effect

First demonstrated the particle nature of light.

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When electromagnetic radiation of sufficient radiation impinges on a metallic surface, electrons are emitted; energy or emission related to frequency of radiation.

E = hv – w

Absorption of Radiation

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(Particle nature of electromagnetic radiation)

Process by which certain frequencies of radiation are removed during passage through a layer of solid, liquid, or gas.

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Results in particles being promoted from a lower-energy state to a higher-energy state–

Each molecule has a discrete number of energy levels, so those energy level differences can be used in spectra as a fingerprint for the molecule.

Two Types of Absorption Fingerprint

Atomic spectra: Relatively simple because due to discrete atomic excitations


Molecular spectra: Complex due to increased excitation states from electronic, vibrational, and rotational excitations.–Broad bands rather than well-defined lines of atomic spectra

Emission of Radiation

 

(Particle Nature of Electromagnetic Radiation)

Energy produced when excited ions, atoms, or molecules return to lower energy or ground states


Particles that are independent of one another (ie-gases) produce discontinuous, line spectrum

Particles that are dependent of one another (ie-liquids or solids) or complicated moleules produce continuous spectrum

Thermal or Blackbody Radiation

Results when solids are heated to incandescence


Continuous radiation emitted is more characterisic of temperature than emitting material

Emission of Gases

Atoms produce a series of discrete lines whose energies correspond to energy differences between electronic energy states


Molecular spectra are more complex because of vibrational or rotational states

X-Ray Emission

Produced when outer electrons fall into a hole created by a lost inner shell electron


Consists of a discrete spectrum superimposed on a continuum


Kα and Kβ: Nondestructive important bands

Resonance Fluorescence Emission

Produced by gaseous atoms and is a situation where the emitted radiation is identical in energy to the excitation energy


Characterized by a time delay of 10-5 seconds or less

Nonresonance Fluorescence Emission
Occurs with molecules in a gaseous or solution state and is a situation where the emitted radiation is lower in energy than excitation energy–results from vibrational relaxation occurring before electronic relaxation, occurs with a time delay of 10-5 seconds or less
Phosphorescence Emission
Occurs when an excited molecule relazes to a metastable excited electronic state which has a lifetime greater than 10-5 seconds

General Design of

Spectroscopic Instrumentation

All contain:

1. Stable source of radiant energy

2. Transparent container for holding the sample

3. Monochromator/wavelength selector that isolates a specific region of the electromagnetic spectrum to be used in the instrument

4. Radiation detector/transducer which converts radiant energy into a usable electrical signal

5. Signal processor and readout which displays the signal on a meter, LED display, o recorder chart

Spectroscopic Instrumentation:

Radiation Sources

Source must generate a beam with the sufficient power for detection and measurement, must generate a stable output (the intensity should not vary with time or with applied voltage)–since power varies exponentially with electrical potential, source must be powered by a regulated power supply (power is lost in excitation)

Spectroscopic Instrumentation:

Continuous Radiation Sources

Generate a continuous band of radiation over a range of wavelengths

 

Usually use deuterium lamps for UV region, use tungsten in visible region

Scattering
Change in direction of radiation as it passes through a transparent medium.
Scattering is in all angles from the original direction of the radiation. 
The larger the particle size in the medium the greater the intensity of scattered radiation. 

Spectroscopic Instrumentation:

Line radiation sources

Emit a few discrete lines of radiation


Mercury and sodium vapor lamps provide sharp lines in the ultraviolet and visible regions


Hollow cahotde lamps used in ataomic absorption provide line spectra for virtually any element

Spectroscopic Instrumentation:

Wavelength Selectors

Provide radiation of limited, narrow, continuous group of wavelengths-bands-required for most spectroscopic analyses

Narrow bandwidth leads to increased sensitivity in absorption measurements and selectivity in emission and absorption methods.

Narrow band of radiation is a necessary criterion for a linear relationship between optical signal and concentration of analyte

Spectroscopic Instrumentation:

Filters

Provide fixed band of wavelengths

Spectroscopic Instrumentation:

Absorption filters

Restricted to the visible region of the spectrum


Function by absorbing certain portions of the spectrum


Commonly consist of colored glass or a dye suspended in a gelatin and sandwiched between glass plates


Effective Bandwidths between 30-250nm

Spectroscopic Instrumentation:

Interference Filters (Definition)

Rely on optical interference to provide radiation of relatively narrow bandwidths (less than 10nm)

 

Used in the UV, visible, and IR regions

Spectroscopic Instrumentation:

Interference filters (Construction)

Consists of a transparent dielectric (CaF2 or MgF2) between two semitransparent metal films which are sandwiched between two plates of glass


Thickness of the dielectric layer determines the wavelength of transmitted radiation

Spectroscopic Instrumentation:

Interference Filters (Principle of Operation)

1. Beam of collimated radiation passes through the glass layer

2.  Fraction passes through 1st metallic layer while remainder is reflected

3. Portion that is tranmitted strikes 2nd metallic layer where a portion is again transmitted and reflected

4. If the reflected portion from the 2nd metallic layer is the proper wavelength, it is partially reflected from the inner side of the first layer in phase with incoming light of the same wavelength

–Light of this wavelength is reinforced and transmitted through the filter while other wavelengths undergo destructive interference

Spectroscopic Instrumentation:

Comparison of Absorption and Interference Filters

Absorption filters are less expensive than interference filters, but are significantly inferior in operation


Absorption filter bandwidths are greater, and for narrow bandwidths, the fraction of light transmitted is less

Spectroscopic Instrumentation:

Monochromators (Definition)

Produce narrow bands of wavelengths continuously variable over a wide range (select a wavelength)

Spectroscopic Instrumentation:

Monochromators (Design)

All contain:

1. Entrance slit

2. Collimating mirror or lens to produce a parallel beam of radiation

3.  Prism or grating which is a dispersing element

4. Focusing mirror or lens

5. Exit slit

Spectroscopic Instrumentation:

Grating Monochromators (General Operation)

Disperse radiation into its wavelengths by operating on the principle of diffraction

 

Grating can either work on principle of transmission or principle of reflection (more common)

Spectroscopic Instrumentation:

Grating Monochromator–

Grating (Construction)

Large number of parallel and closely spaced grooves blazed on a hard, polished surface


For UV-Vis: 300-2000 grooves/nm

For IR: 10-200 grooves/nm


Constructed with relatively broad faces from which reflection occurs and narrow unused faces; each broad face can be considered as a point source of radiation from which interference of reflected beams can occur–for constructive interference, path difference between reflected beams must be integral multiple of wavelengths

Spectroscopic Instrumentation:

Prism Monochromator

Operate on the principle of refraction to disperse radiation into its wavelengths

Spectroscopic Instrumentation:

Comparison of Grating and Prism Monochromators

1. Dispersion (variation of wavelength as a function of distance along the focal plane) of grating monochromator is independent of wavelength, while prism is not; this makes design of grating simpler

2.  Fixed dispersion of grating makes it easy to scan entire spectrum at constant bandwidth since slits need only be adjusted on onset.

–narrower slit widths are required on grating at shorter wavelengths if bandwidth is to be kept constant; narrower slit widths produce better resolution

3.  Better dispersion can be expected from grating

4.  Grating produces greater amounts of stray radiation (scattering) as well as higher-order spectra

5. Comparable in cost

Spectroscopic Instrumentation:

Sample Containers (required for all studies except emission spectroscopy)

Cells or cuvettes that hold samples


Must be made of a material that passes radiation in the spectral region of interest

Quartz or fused silica required for work in the UV region

Silicate and plastic can be used in visible region

Crystalline NaCl most common in IR region

Spectroscopic Instrumentation:

Radiation Detectors (Characteristics)

Should have:

1. High sensitivity

2. High signal-to-noise ratio

3. Constant response over a wide wavelength range

4. Fast response time

5. Minimal dark current (response in absence of illumination)

6. Response that is directly proportional to radiant power

***Two types:  Photoelectric detectors and infrared detectors

Spectroscopic Instrumentation:

Photoelectric detectors

All based on a photoactive surface that:

1. Absorbs radiation

2. Emits elections because of radiation absorption


These 2 things produce a photocurrent which is measured

Spectroscopic Instrumentation:

Photoelectric Detectors–Photovoltaic Cells

Used to detect and measure visible radiation (350-750 nm)

Consist of a flat copper or iron electrode upon which is deposited a layer of semiconducting material, (Se or Cu2O); outer surface of semiconductor coated with thin transparent metallic film of Au or Ag (serves as 2nd/collector electrode)

When radiation of sufficient energy falls on semiconductor, electrons freed proportional to # of photons striking material

Cells are rugged and low cost, no external power souce required, but lack sensitivity at low levels of illumination & during continued illumination, current output will decrease

Spectroscopic Instrumentation:

Photoelectric Detectors–Phototubes

Consist of: semicylindrical cathode and a wire anode sealed inside an evacuated transparent tube.
Cathode has a layer of photoemissive material which emits electrons upon illumination.

Potential applied across the electrodes causing the emitted electrons to flow to the anode generating a photocurrent. 
Photocurrents are about 0.1 those of the photocells but can be easily amplified.

The number of electrons ejected from the cathode is directly proportional to the power of the radiant beam. 
Have a small dark current due to thermally induced electron emission and natural radioactivity from 40K in the glass housing of the tube.

Spectroscopic Instrumentation:

Photoelectric Detectors–Photomultiplier Tubes

Used for measurement of low radiation power

Consists of arrangement of 9 phototubes in series (dynodes), each dynode is 90V more positive than last dynode, which accelerates electrons and emits more photons after each pass

Typically 106-107 more electrons formed for each photon that strikes cathode

Sensitive to UV-Vis radiation, fast response times, relatively large dark currents (eliminated by cooling device to -30°)

Spectroscopic Instrumentation:

Signal Processors

Electronic amplifiers which amplify electrical signal from detector and may change the DC signal to AC signal for filtering/removing noise


May also electronically differentiate or integrate signal

Spectroscope

Optical instrument which contain monochromator in which exit slit has been replaced by an eyepiece that can be moved along focal plane


Used to visually determine wavelength of an emission by measuring angle between incident and dispersed beam when line is centered on eyepiece

Colorimeter

Instruments for adsorption measurement in which the human eye serves as a detector


Color of the unknown visually compared to color of standard solution

Photometer
Fixed wavelength instruments which contain a radiation source, a filter, and a photoelectric detector plus a signal processor and readout
Fluorometer
Photometer designed for fluorescence measurements
Spectrographs

Instruments which contain a monochromator in which the focal plane is made up of a holder for a photographic film or plate

 

All wavelengths are measured simultaneously

Spectrometer

Instrument which contains a fixed slit in the focal plane

 

If equipped with a photoelectric detector, it is called a spectrophotometer

Spectrophotometer
Spectrometer equipped with a photoelectric detector

Absorption Spectroscopy:

Two Considerations in Instrumental Design

1. Location of the sample and reference cells with respect to the wavelength selector


2. Timing of the measurement of the incident and transmitted power (intensity) of the radiation as well as dark current

Absorption Spectroscopy:

Two Arrangements of Sample and Reference Cells

1. Between the source and wavelength selector

 

2. Between wavelength selector and detector

Absorption Spectroscopy:

Relative Advantages and Disadvantages of Placing Sample and Reference Cells between Source and Wavelength Selector

**All of the radiation from the source passes through sample

+1. Scattering of radiation by the components of the sample does not interfere with analysis because they are subsequently rejected by the monochromator and do not reach detector

-2. Shorter wavelengths of radiation from the source are available to induce fluorescence in the sample which will produce an emission spectrum that will interfere with absorption measurements

-3. The shorter wavelengths often cause photodecomposition of the sample, interfering with measurement.

Absorption Spectroscopy:

Relative Advantages and Disadvantages of Placing Sample and Reference Cells between Wavelength Selector and Detector

**Only selected wavelength passes through sample

+1. Interference from fluorescence and photodecomposition are minimized because the shorter wavelengths have been removed before sample is irridated.

-2. Scattering results in errors

*Scattering errors are less serious than fluorescence and photodecomposition errors (from other arrangement) so this arrangement is preferred

Absorption Spectroscopy:

Single Beam Instrumentation

Has one beam of radiation that passes from source through wavelength selector and to detector

Measurement involves setting 0%T w/shutter in place, adjustment of 100%T with blank, then measurement of T for sample

Reliability of measurement depends on constancy of instrumental characteristics during measurement process–hence time required to complete measurement is kept as small as possible

Absorption Spectroscopy:

Double-beam Instrumentation (General)

Have two beams of radiation; one passes through sample and other passes through reference

Two types of double beam instrument:

1. Double beam in position

2. Double beam in time

Absorption Spectroscopy:

Double Beam Instrument, in Position

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Absorption Spectroscopy:

Double Beam Instrumentation–in Time

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Absorption Spectroscopy:

Relative Advantages and Disadvantages of Single-Beam vs. Double-Beam Instrumentation

1. In double-beam instruments, because measurement of incident and transmitted radiation is made simultaneously, drift in power of source and noise from detector is compensated for–good performance from lower quality instruments can be obtained

2. Double-beam allows spectra to be recorded (in single-beam, must manually change wavelength)

3. Double-beam is more complex, requires more components

4. Single-beam are simpler, lower in cost, and more portable

5. Single-beam instruments have higher S/N ratios than double-beam because more radiant energy reaches detector

Absorption Spectroscopy:

Multichannel Instrumentation

Single-beam design, but use a photodiode array or linear charge-coupled-device (CCD)

Dispersive system placed after sample and reference cell

Measurement: Dark current is stored and subtracted from sample cell reading

Absorption Spectroscopy:

Equations for Transmittance and Absorbance

Transmittance:

T = P/P0

where P = Power after, P0= Power before

Absorbance:

A = -logT = log P/P0

Absorbance Spectroscopy:
Beer’s Law (Equation and Assumptions)

A = εbc

where ε = molar absorptivity in L/mol*cm

b = path length in cm

c = analyte concentration in mol/L

Assumes:

1. Incident radiation is monochromatic

2. Absorption occurs in volume of uniform cross section

3. Absorbing substances behave independently of one another in absorption process

Absorption Spectroscopy:

Limitations to Beer’s Law–Real Factors

1. Describes behavior in dilute solutions.  At high concentrations (>.01M), distance between species responsible for absorption is lessened to the point where each affects charge distribution of neighbors, which in turn alters their ability to absorb given wavelength of radiation.

2. Molar absorptivities are dependent upon the refractive index of solution.  Negative deviation in concentration changes cause significant change in refractive index of solution (Must use linear range)

Absorption Spectroscopy:

Limitations to Beer’s Law–Instrumental Factors

–Always lead to negative absorbance errors

1. Polychromatic radiation: If a beam consists of two wavelengths λ and λ’:

P0/P = 10εbc

P’0/P = 10ε’bc

and measured absorbance is:

A = log(P0+P’0)/(P+P)

= log(P0+P’0)/(P010-εbc+P’010-ε’bc)

Therefore, ε must = ε’ for Beer’s Law to apply

2. Stray radiation: Decreases apparent absorbance, leads to negative deviation

3. Instrumental noise: Limites working transmittance rance from 10-80% to keep concentration errors between 1-2%

Absorption Spectroscopy:

Limitations to Beer’s Law–Chemical factors

Deviations result from:

1. Dissociation

2. Association

3. Complex formation

4. Polymerization

5. Solvolysis

–Absorbing species reacts to produce product with an absorption spectrum different from that of analyte (ex-Weak acid dilution: more dilute the solution, lower the absorbance)

UV-Vis Spectroscopy:

Nature of Absorption Process

Two step process (for species M):

1. Excitation: Usually from the ground electronic state to a higher electronic state

M + hν –> M*

–Lifetime of the excited state is brief (10-8 to 10-9 sec)

2.  Relaxation: Either conversion of excitation energy to heat

M* –> M + heat

or decomposition of M* to form a new species of fluorescent or phosphorescent reemission of radiation

–Because energetic differences between vibrational and rotational levels in the electronic states are small, the many possible energy differences between two electronic states overlap, causing braod absorptive bands for polyatomic species

–Bandwidths are 50nm or more

UV-Vis Spectroscopy:

Electronic Transitions–Types of

Molecular Orbitals

1. Bonding orbitals: Increase the stability of a molecule, leading to increased electron density between atoms.

2. Sigma (σ) orbitals: Symmetrical along the internuclear axis; correspond to single bonds between atoms.

3. Pi (π) orbitals: Formed by side-by-side overlap of p orbitals, not symmetrical along internuclear axis but form cloud of electrons above and below axis.

4. Nonbonding (n) orbitals: Consist of unshared electron pairs from atomic orbitals not associated w/bonding in molecule.

5. Antibonding orbitals (*): Decrease the molecular stability leading to increased electron density outside the area between atoms.

UV-Vis Spectroscopy:

Possible Electronic Transitions

*Arranged in order of most energetic to least:

σ–>σ* transitions occur in the vacuum UV at wavelengths below 150nm; characteristic of transitions associated with C-H and C-C bonds, occur outside range of most instruments

n–>σ* transitions occur in the 150-250nm region and are typical of organic molecules containing a heteroatom (N,O,S,F,Cl,Br,or I)

π–>π* transitions occur in the 180-700nm range and are typical of molecules that exhibit some degree of unsaturation (double/triple bonds, aromatic rings); strongest of absorptions having absorptivities ranging from 1000-15,000

n–>π* transitions occur in the 180-700nm molecules that contain C=O, N=N, N=O, or NO2; occur between a nonbonding orbital and an antibonding π orbital associated with a double or triple bond in the molecule

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