1. 1.0 Basic Concepts and Definitions
signals, noise, and the signal-to-noise ratio (SNR or S/N)
definition of basic terms
calibration graph terms
types of measurements
hypothesis testing
general observations about signal-to-noise enhancement
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2. The Signal-to-Noise Ratio
The central theme of CHM 621 is the improvement of measurements in analytical chemistry. No matter how well any technique performs, a problem will be encountered or a restriction imposed which requires measurements pushing the state of the art.
Improvements in measurements are ordinarily achieved by enhancing the signal-to-noise ratio.
signal: that part of the measured response which provides the desired information
noise: any random variation in the response
signal-to-noise ratio: the signal divided by the noise
There are two obvious strategies: increase the signal faster than the noise; and, decrease the noise faster than the signal.
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3. Definition of Basic Terms
Method-related terms.
sample: the physical entity being examined
analyte: that part of the sample which is being identified or quantified
matrix: the material within which the analyte is found
determine: this word should be coupled with the analyte - manganese is determined by x-ray fluorescence
analyze: this word should be coupled with the sample - an alloy is analyzed for manganese
Measurement-related terms.
blank: the measured response when a sample is examined that is believed to contain nothing which should produce the signal
interference: a non-random part of the measurement which does not arise from the analyte
Blanks and interferences are difficult to removed by signal averaging strategies.
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4. Specificity
Specificity implies that an analytical method is specific for a given analyte.
if a method were truly specific no other compound would falsely contribute to the measured response, e.g. there would be no blank or interference
very few specific methods exist when the whole universe of possible compounds needs to be considered
the better the sample is characterized, the easier it is to find a method specific for a given analyte
a method might be specific for a compound found in one sample, but be non-specific when analyzing another type of sample
The lack of specificity is why there are many analytical methods for determining the same compound.
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5. Selectivity
Selectivity implies that an analytical method can select among several possible analytes and ascertain which is producing the measured response.
methods with great selectivity produce multi-dimensional data rich in features and/or possess high resolving power
methods that are selective can identify or quantify several analytes at the same time
the existence of a blank is due to a level of selectivity too low to distinguish the analyte from other sample components
methods with great selectivity will often produce more data than are necessary for testing the analytical hypothesis
Methods that use selectivity to quantify multiple analytes are preferable to multiple methods each specific for one analyte.
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6. Sensitivity
Sensitivity is the slope of the calibration graph - the change in the response per unit change in analyte concentration or amount.
In the graph at the right, method A has a sensitivity of 1 V M-1, while B has a sensitivity of
0.5 V M-1. Method A is twice as sensitive as method B.
In order to state that one method of analysis is more sensitive than another, they must both have the same y-axis units.
Sensitivity is not necessarily related to the lowest measurable concentration or amount.
An increase in sensitivity usually requires a concomitant increase in selectivity.
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7. Calibration Graph Terms
The limit of detection is the lowest concentration or amount that can produce a signal distinguishable from the noise. By convention this is the response with a SNR = 3. For the graph the LOD is ~0.6 mM.
The dynamic range of a calibration graph is the range of concentrations from the LOD up to the largest yielding a unique response without sample dilution. The linear dynamic range is that from the LOD to the largest which is linearly related to the measured response.
Sensitivity is often erroneously used to describe the limit of detection.
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8. Qualitation
qualitation is the process of determining the identity of sample constituents with no regard to how much may be present (this includes structural determinations)
speciation involves identifying molecules in a sample which include certain elements, functional groups or moieties
qualitation can be subdivided into three categories
if an excellent idea already exists about the identity of a sample component, confirmation is all that may be needed - redundant data are often used (sodium doublet)
recognition occurs when there is a good reason to believe that the sample has been seen before - archival data sets are often used (searching infrared spectral collections)
ab initio identification is qualitation when no reference data are available (multiple methods are used to build up the molecular structure)
All attempts at qualitation will fail unless the sample is pure!
Qualitation often requires an SNR much larger than that for the LOD.
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9. Quantitation
quantitation is the process of determining the amount or concentration of one or more sample components
amount can be expressed as moles or molecules
concentration can be expressed as moles per liter (molarity) or molecules per cubic centimeter (number density)
to improve sensitivity the measured parameter can be the result of an amplification process such as catalysis (enzymes) or multiple interactions with a single analyte molecule (photon bursts)
the ultimate in quantitation is single molecule detection
first report of single atoms in 1977
first report of single molecules in 1984
1990 was the approximate date when single molecule detection became "routine"
of increasing importance is the spatial or temporal variations of the analyte throughout the sample
The fundamental limit to precision is determined by fluctuations in the amount of sample being observed.
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10. Hypotheses and Information
analytical chemistry is the discipline concerned with testing hypotheses utilizing knowledge of the composition of matter
analytical procedures are the chemical and instrumental measurements used to obtain relevant data
the amount of information produced by a given procedure can be determined by the decrease in uncertainty concerning the composition of matter, as long as that decrease serves to test the stated hypothesis
the definition of information uses the phrase, "decrease in uncertainty," because there must be some prior knowledge about the sample
information by exclusion, e.g. the sample contains hydrocarbons
origin of the sample
knowledge of the theory behind the measurement
some hypotheses are impossible to test
The information content of an analytical procedure is most often increased by enhancing the SNR.
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11. Information and Data
data are the set of measured responses arising from the analyte
information is that portion of the data that is used to test the hypothesis
the size of the data in bits is ordinarily larger than the information content in bits
example: if the data are a set of values only differing by random noise, most of the information in the data is contained in the mean and standard deviation
larger than necessary data sets are often collected for convenience, e.g. an entire spectrum
different portions of the same data set may contain information about different hypotheses
example: in the infrared, the fingerprint region would be preferred for recognition, whereas characteristic frequencies would be favored for ab initio identification
An analytical method should be chosen that maximizes the fraction of the data that contains information.
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12. Assigning Sensitivity
Consider quantifying a compound using absorption spectrophotometry, A = elC. The calibration curve involves plotting absorbance, A, versus concentration, C. Sensitivity is given by the slope of the calibration curve, e.g. el, where e is the molar absorptivity, and l is the pathlength.
the instrumental portion of the sensitivity is given by the pathlength
the molecular portion of the sensitivity is given by the molar absorptivity
sensitivity could be increased by derivatizing the analyte to increase the molar absorptivity, or by increasing the size of the sample cell
signal-to-noise enhancement of the measured absorption will improve the limit of detection, but not the sensitivity
Fluorescence measurements are often said to be more sensitive than absorption measurements. This is incorrect since the number of emitted photons can never exceed the number absorbed.
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13. Not Enhancing the SNR
Don't improve the SNR of a measurement beyond the normal sample-to-sample variation. A well known example was work in clinical chemistry where new techniques proposed by analytical chemists often had a SNR much better than the normal range of healthy patients.
Don't try to increase information content by improving the SNR when a change in method would be more fruitful. This is a particularly bad phenomenon in academia, where research groups are technique oriented.
Don't use mathematical techniques to extract the needed information from a large data set unless it is absolutely necessary. It is amusing to think about all the matrix algebra and advanced curve fitting techniques developed to perform multicomponent analyses when the sample could have easily been analyzed by chromatography.
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