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CHAPTER 1 FUNDAMENTAL CONCEPTS 1. This course covers: The fundamentals of common analytical instruments Measurements with these instruments Interpretation.

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Presentation on theme: "CHAPTER 1 FUNDAMENTAL CONCEPTS 1. This course covers: The fundamentals of common analytical instruments Measurements with these instruments Interpretation."— Presentation transcript:


2 This course covers: The fundamentals of common analytical instruments Measurements with these instruments Interpretation of data obtained from the measurements Communication of the meaning of the results INSTRUMENTAL ANALYSIS 2

3 WHAT IS ANALYTICAL CHEMISTRY The qualitative and quantitative characterization of matter The scope is very wide and it is critical to our understanding of almost all scientific disciplines Characterization Qualitative: The identification of chemical compounds or elements present in a sample Quantitative: the determination of the exact amount of compound or element present in a sample Chemical Species Could be an element, ion or compound (organic or inorganic) 3

4 Bulk Analysis Characterization of the entire sample Example: determination of the elemental composition of a mixture (alloys) Surface Analysis Characterization of the surface of a sample Example: finding the thickness of a thin layer on the surface of a solid material Characterization may also include Structural Analysis and measurement of physical properties of materials CHATACTERIZATION 4

5 WET CHEMICAL ANALYSIS Also called Classical methods Separation of component of interest (analyte) from the sample by precipitation, extraction, or distillation, followed by gravimetric or titrimetric measurement for quantitative analysis Wet analysis is time consuming and demands attention to detail Volumetric Analysis Analysis by volume Gravimetric Analysis Analysis by mass Examples Acid-base titrations, redox titrations, complexometric titrations, precipitation reactions 5

6 Nondestructive Analysis Useful when evidence needs to be preserved Used to analyze samples without destroying them Examples Forensic analysis Paintings WET CHEMICAL ANALYSIS 6

7 Instrumental Methods Involve interactions of analyte with EMR (electromagnetic radiation) –Radiant energy is either produced by the analyte (e.g., Auger) or changes in EMR are brought about by its interaction with the sample (e.g., NMR) Other methods include measurement of electrical properties (e.g., potentiometry) 7

8 Instruments Converts information stored in the physical or chemical characteristics of the analyte into useful information Require a source of energy to stimulate measurable response from analyte Data domains –Methods of encoding information electrically –Nonelectrical domains –Electrical domains Analog, Time, Digital 8

9 Instruments Detector –Device that indicates a change in one variable in its environment (eg., pressure, temp, particles) –Can be mechanical, electrical, or chemical Sensor –Analytical device capable of monitoring specific chemical species continuously and reversibly Transducer –Devices that convert information in nonelectrical domains to electrical domains and the converse 9

10 Selecting an Analytical Method What accuracy is required How much sample is available What is the concentration range of the analyte What components of the sample will cause interference What are the physical and chemical properties of the sample matrix How many samples are to be analyzed 10

11 THE ANALYTICAL APPROACH Problems continuously occur around the world in Manufacturing industries The environment The health sector (medicine) etc. The analytical chemist is the solution to these problems The analytical chemist must understand the analytical approach uses, capabilities, and limitations of analytical techniques 11

12 Analyte A substance to be measured in a given sample Matrix Everything else in the sample Interferences Other compounds in the sample matrix that interfere with the measurement of the analyte THE ANALYTICAL APPROACH 12

13 Homogeneous Sample Same chemical composition throughout (steel, sugar water, juice with no pulp, alcoholic beverages) Heterogeneous Sample Composition varies from region to region within the sample (pudding with raisins, granola bars with peanuts) Differences in composition may be visible or invisible to the human eye (most real samples are invisible) Variation of composition may be random or segregated THE ANALYTICAL APPROACH 13

14 Analyze/Analysis Applied to the sample under study Determine/Determination Applied to the measurement of the analyte in the sample Multiple Samples Identically prepared from another source Replicate Samples Splits of sample from the same source THE ANALYTICAL APPROACH 14

15 General Steps in Chemical Analysis 1.Defining the problem (formulating the question) To be answered through chemical measurements 2.Selecting techniques (designing the analytical method) Find appropriate analytical procedures 3.Sampling and sample storage Select representative material to be analyzed 4.Sample preparation Convert representative material into a suitable form for analysis THE ANALYTICAL APPROACH 15

16 General Steps in Chemical Analysis 5.Analysis (performing the measurement) Measure the concentration of analyte in several identical portions 6.Assessing the data 7.Method validation 8.Documentation THE ANALYTICAL APPROACH 16

17 DEFINING THE PROBLEM Find out the information that needs to be known about a sample (or what procedure is being studied) How accurate and precise the information must be Whether qualitative or quantitative analysis or both is required How much sample is available for study Whether nondestructive analysis must be employed 17

18 Bulk analysis or analysis of certain parts is required Sample is organic or inorganic Sample a pure substance or a mixture Homogeneous or heterogeneous sample Chemical information or elemental information needed DEFINING THE PROBLEM 18

19 Qualitative Analysis Provides information about what is present in the sample If quantitative analysis is required, qualitative analysis is usually done first Capabilities and limitations of analysis must be well understood DEFINING THE PROBLEM 19

20 Qualitative Analysis Qualitative Elemental Analysis Used to identify elements present in a material Can provide empirical formula of organic compounds (X- Ray Fluorescence, AAS) Qualitative Molecular Analysis Used to identify molecules present in a material Can be used to obtain molecular formula Can be used to distinguish between isomers (NMR, IR, MS) DEFINING THE PROBLEM 20

21 Qualitative Analysis Empirical Formula The simplest whole number ratios of atoms of each element present in a molecule Molecular Formula Contains the total number of atoms of each element in a single molecule of the compound Isomers Different structures with the same molecular formula (n- butane and iso-butane) DEFINING THE PROBLEM 21

22 Qualitative Analysis Enantiomers Nonsuperimposable mirror-image isomers Said to be chiral Have the same IR, NMR, and MS Mostly same physical properties (boiling-point, melting point, refractive index) Chiral Chromatography can be used to distinguish between such optically active compounds (erythrose, glyceraldehyde) DEFINING THE PROBLEM 22

23 Qualitative Analysis Mixtures of Organic Compounds Mixtures are usually separated before the individual components are identified Separation techniques include GC LC HPLC CE DEFINING THE PROBLEM 23

24 Quantitative Analysis The determination of the amount of analyte in a given sample Often expressed in terms of concentrations Concentration The quantity of analyte in a given volume or mass of sample Molarity = moles/liters, ppm = µg/g sample ppb = ng/g sample, ppt = pg/g sample Percent by mass [%(m/m)], Percent by volume [%(v/v)] DEFINING THE PROBLEM 24

25 Quantitative Analysis Early methods include volumetric, gravimetric, and combustion analysis Automated and extremely sensitive methods are being used today (GC, IR, HPLC, CE, XRD) Require micron amounts and a few minutes Hyphenated techniques are used for qualitative and quantitative measurements of the components mixtures (GC-MS, LC-MS) DEFINING THE PROBLEM 25

26 DESIGNING THE ANALYTICAL METHOD Analytical procedure is designed after the problem has been defined Analyst must consider Accuracy and precision Amount of sample to be used Cost analysis Turnaround time (time between receipt of sample and delivery of results) 26

27 Green chemistry processes preferred for modern analytical procedures The goal is to minimize waste and pollution Use of less toxic or biodegradable solvents Use of chemicals that can be recycled Standard methods are available in literature (reproducible with known accuracy and precision) DESIGNING THE ANALYTICAL METHOD 27

28 Do not waste time developing a method that already exists Method of choice must be reliable and robust Interferences must be evaluated Interference Element or compound that respond directly to measurement to give false analyte signal Signal may be enhanced or suppressed DESIGNING THE ANALYTICAL METHOD 28

29 Fundamental Features of Method A blank must be analyzed The blank is usually the pure solvent used for sample preparation Used to identify and correct for interferences in the analysis Analyst uses blank to set baseline Reagent blank: contains all the reagents used to prepare the sample Matrix blank: similar in chemical composition to the sample but without the analyte DESIGNING THE ANALYTICAL METHOD 29

30 Fundamental Features of Method Methods require calibration standards (except coulometry) used to establish relationship between analytical signal being measured and the concentration of analyte This relationship (known as the calibration curve) is used to determine the concentration of unknown analyte in samples DESIGNING THE ANALYTICAL METHOD 30

31 Fundamental Features of Method Reference (check) standards are required Standards of known composition with known concentration of analyte Run as a sample to confirm that the calibration is correct Used to access the precision and accuracy of the analysis Government and private sources of reference standards are available (National Institute of Standards and Technology, NIST) DESIGNING THE ANALYTICAL METHOD 31

32 Sampling and Sample Preparation 32

33 The most important step is the collection of the sample of the material to be analyzed Sample should be representative of the material Sample should be properly taken to provide reliable characterization of the material Sufficient amount must be taken for all analysis Representative Sample Reflects the true value and distribution of analyte in the original material SAMPLING 33

34 Steps in Sampling Process Gross representative sample is collected from the lot Portions of gross sample is taken from various parts of material Sampling methods include Long pile and alternate shovel (used for very large lots) Cone and quarter Aliquot Quantitative amount of a test portion of sample solution SAMPLING 34

35 Care must be taken since collection tools and storage containers can contaminate samples Make room for multiple test portions of sample for replicate analysis or analysis by more than one technique Samples may undergo grinding chopping milling cutting SAMPLING 35

36 Gas Samples Generally considered homogeneous Samples are stirred before portions are taken for analysis Gas samples may be filtered if solid materials are present Grab samples Samples taken at a single point in time Composite Samples Samples taken over a period of time or from different locations SAMPLING 36

37 Gas Samples Scrubbing Trapping an analyte out of the gas phase Examples Passing air through activated charcoal to adsorb organic vapors Bubbling gas samples through a solution to absorb the analyte Samples may be taken with Gas-tight syringes Ballons (volatile organic compounds may contaminate samples) Plastic bags (volatile organic compounds may contaminate samples) Glass containers (may adsorb gas components) SAMPLING 37

38 Liquid Samples May be collected as grab samples or composite samples Adequate stirring is necessary to obtain representative sample Stirring may not be desired under certain conditions (analysis of oily layer on water) Undesired solid materials are removed by filtration or centrifugation Layers of immiscible liquids may be separated with the separatory funnel SAMPLING 38

39 Solid Samples The most difficult to sample since least homogeneous compared to gases and liquids Large amounts are difficult to stir Must undergo size reduction (milling, drilling, crushing, etc.) to homogenize sample Adsorbed water is often removed by oven drying SAMPLING 39

40 Sample Storage Samples are stored if cannot be analyzed immediately Sample composition can be changed by interaction with container material, light, or air Appropriate storage container and conditions must be chosen Organic components must not be stored in plastic containers due to leaching Glass containers may adsorb or release trace levels of ionic species SAMPLING 40

41 Sample Storage Appropriate cleaning of containers is necessary Containers for organic samples are washed in solvent Containers for metal samples are soaked in acid and deionized water Containers must be first filled with inert gas to displace air Biological samples are usually kept in freezers Samples that interact with light are stored in the dark SAMPLING 41

42 Sample Storage Some samples require pH adjustment Some samples require addition of preservatives (EDTA added to blood samples) Appropriate labeling is necessary Computer based Laboratory Information Management Systems (LIMS) are used to label and track samples SAMPLING 42

43 SAMPLE PREPARATION Make samples in the physical form required by the instrument Make concentrations in the range required by the instrument Free analytes from interfering substances Solvent is usually water or organic 43

44 Type of sample preparation depends on nature of sample technique chosen analyte to be measured the problem to be solved Samples may be dissolved in water (or other solvents) pressed into pellets cast into thin films etc. SAMPLE PREPARATION 44

45 Acid Dissolution and Digestion Used for dissolving metals, alloys, ores, glass, ceramics Used for dissolving trace elements in organic materials (food, plastics) Concentrated acid is added to sample and then heated Choice of acid depends on sample to be dissolved and analyte Acids commonly used: HCl, HNO 3, H 2 SO 4 HF and HClO 4 require special care and supervision SAMPLE PREPARATION METHODS 45

46 Fusion (Molten Salt Fusion) Heating a finely powdered solid sample with a finely powdered salt at high temperatures until mixture melts Useful for the determination of silica-containing minerals, glass, ceramics, bones, carbides Salts (Fluxes) Usually Used Sodium carbonate, sodium tetraborate (borax), sodium peroxide, lithium metaborate SAMPLE PREPARATION METHODS 46

47 Dry Ashing and Combustion Burning an organic material in air or oxygen Organic components form CO 2 and H 2 O vapor leaving inorganic components behind as solid oxides Cannot be used for the determination of mercury, arsenic, and cadmium SAMPLE PREPARATION METHODS 47

48 Extraction Used for determining organic analytes Makes use of solvents Solvents are chosen based on polarity of analyte (like dissolves like) Common Solvents Hexane, xylene, methylene chloride SAMPLE PREPARATION METHODS 48

49 Solvent Extraction Based on preferential solubility of analyte in one of two immiscible phases For two immiscible solvents 1 and 2 The ratio of concentration of analyte in the two phases is approximately constant (K D ) SAMPLE PREPARATION METHODS 49

50 Solvent Extraction Large K D implies analyte is more soluble in solvent 1 than in solvent 2 Separatory funnel is used for solvent extraction Percent of analyte extracted (%E) V 1 and V 2 are volumes of solvents 1 and 2 respectively SAMPLE PREPARATION METHODS 50

51 Solvent Extraction Multiple small extractions are more efficient than one large extraction Extraction instruments are also available Examples Extraction of pesticides, PCBs, petroleum hydrocarbons from water fat from milk SAMPLE PREPARATION METHODS 51

52 Other Extraction Approaches Microwave Assisted Extraction Heating with microwave energy during extraction Supercritical Fluid Extraction (SFE) Use of supercritical CO 2 to dissolve organic compounds Low cost, less toxic, ease of disposal Solid Phase Extraction (SPE) Solid Phase Microextraction (SPME) The sample is a solid organic material Extracted by passing sample through a bed of sorbent (extractant) SAMPLE PREPARATION METHODS 52

53 Statistics 53

54 STATISTICS Statistics are needed in designing the correct experiment Analyst must select the required size of sample select the number of samples select the number of replicates obtain the required accuracy and precision Analyst must also express uncertainty in measured values to understand any associated limitations know significant figures 54

55 STATISTICS Rules For Reporting Results Significant Figures = digits known with certainty + first uncertain digit The last sig. fig. reflects the precision of the measurement Report all sig. figs such that only the last figure is uncertain Round off appropriately (round down, round up, round even) 55

56 STATISTICS Rules For Reporting Results Report least sig. figs for multiplication and division of measurements (greatest number of absolute uncertainty) Report least decimal places for addition and subtraction of measurements (greatest number of absolute uncertainty) The characteristic of logarithm has no uncertainty Does not affect the number of sig. figs. Discrete objects have no uncertainty Considered to have infinite number of sig. figs. 56

57 ACCURACY AND PRECISION Accuracy is how close a measurement is to the true (accepted) value True value is evaluated by analyzing known standard samples Precision is how close replicate measurements on the same sample are to each other Precision is required for accuracy but does not guarantee accuracy Results should be accurate and precise (reproducible, reliable, truly representative of sample) 57

58 ERRORS Two principal types of errors: Determinate (systematic) and indeterminate (random) Determinate (Systematic) Errors Caused by faults in procedure or instrument Fault can be found out and corrected Results in good precision but poor accuracy May be constant (incorrect calibration of pH meter or mass balance) variable (change in volume due to temperature changes) additive or multiplicative 58

59 Examples of Determinate (Systematic) Errors Uncalibrated or improperly calibrated mass balances Improperly calibrated volumetric flasks and pipettes Analyst error (misreading or inexperience) Incorrect technique Malfunctioning instrument (voltage fluctuations, alignment, etc) Contaminated or impure or decomposed reagents Interferences ERRORS 59

60 To Identify Determinate (Systematic) Errors Use of standard methods with known accuracy and precision to analyze samples Run several analysis of a reference analyte whose concentration is known and accepted Run Standard Operating Procedures (SOPs) ERRORS 60

61 Indeterminate (Random) Errors Sources cannot be identified, avoided, or corrected Not constant (biased) Examples Limitations of reading mass balances Electrical noise in instruments ERRORS 61

62 Random errors are always associated with measurements No conclusion can be drawn with complete certainty Scientists use statistics to accept conclusions that have high probability of being correct and to reject conclusions that have low probability of being correct Random errors follow random distribution and analyzed using laws of probability Statistics deals with only random errors Systematic errors should be detected and eliminated ERRORS 62

63 THE GAUSSIAN DISTRIBUTION Symmetric bell-shaped curve representing the distribution of experimenal data Results from a number of analysis from a single sample follows the bell-shaped curve Characterized by mean and standard deviation 63

64 a is the height of the curve’s peak µ is the position of the center of the peak (the mean) σ is a measure of the width of the curve (standard deviation) T (or x t ) is the accepted value The larger the random error the broader the distribution There is a difference between the values obtained from a finite number of measurements (N) and those obtained from infinite number of measurements THE GAUSSIAN DISTRIBUTION 64

65 THE GAUSSIAN DISTRIBUTION f(x) a μ x -σ-σσ-2σ-3σ2σ2σ3σ3σ f(x) = frequency of occurrence of a particular results T (x t ) Point of inflection 65

66 Arithmetic mean of a finite number of observations Also known as the average Is the sum of the measured values divided by the number of measurements ∑x i = sum of all individual measurements x i x i = a measured value N = number of observations SAMPLE MEAN 66

67 The limit as N approaches infinity of the sample mean µ = T in the absence of systematic error POPULATION MEAN (µ) 67

68 Total error = sum of all systematic and random errors Relative error = absolute error divided by the true value ERROR 68

69 Relative deviation (D) = absolute deviation divided by mean STANDARD DEVIATION Percent Relative deviation [D(%)] 69

70 Sample Standard Deviation (s) A measure of the width of the distribution Small standard deviation gives narrow distribution curve For a finite number of observations, N x i = a measured value N = number of observations N-1 = degrees of freedom STANDARD DEVIATION 70

71 Population Standard Deviation (σ) For an infinite number of measurements Standard Deviation of the mean (s m ) Standard deviation associated with the mean consisting of N measurements STANDARD DEVIATION 71

72 Percent Relative Standard Deviation (%RSD) STANDARD DEVIATION Variance Is the square of the standard deviation Variance = σ 2 or s 2 Is a measure of precision Variance is additive but standard deviation is not additive Total variance is the sum of independent variances 72

73 Median The middle number in a series of measurements arranged in increasing order The average of the two middle numbers if the number of measurements is even Mode The value that occurs the most frequently Range The difference between the highest and the lowest values QUANTIFYING RANDOM ERROR 73

74 The Gaussian distribution and statistics are used to determine how close the average value of measurements is to the true value The Gaussian distribution assumes infinite number of measurements for N > 20 The standard deviation coincides with the point of inflection of the curve (2 inflection points since curve is symmetrical) QUANTIFYING RANDOM ERROR 74

75 f(x) a μ x -σ-σσ-2σ-3σ2σ2σ3σ3σ Population mean (µ) = true value (T or x t ) x = µ Points of inflection QUANTIFYING RANDOM ERROR 75

76 Range µ ± 1σ µ ± 2σ µ ± 3σ Gaussian Distribution (%) 68.3 95.5 99.7 Probability Range of measurements for ideal Gaussian distribution The percentage of measurements lying within the given range (one, two, or three standard deviation on either side of the mean) QUANTIFYING RANDOM ERROR 76

77 The average measurement is reported as: mean ± standard deviation Mean and standard deviation should have the same number of decimal places In the absence of determinate error and if N > 20 68.3% of measurements of x i will fall within x = µ ± σ (68.3% of the area under the curve lies in the range of x) 95.5% of measurements of x i will fall within x = µ ± 2σ 99.7% of measurements of x i will fall within x = µ ± 3σ QUANTIFYING RANDOM ERROR 77

78 f(x) a μ x -σ-σσ-2σ-3σ2σ2σ3σ3σ 68.3% known as the confidence level (CL) x = µ ± σ QUANTIFYING RANDOM ERROR 78

79 f(x) a μ x -σ-σσ-2σ-3σ2σ2σ3σ3σ 95.5% known as the confidence level (CL) x = µ ± 2σ QUANTIFYING RANDOM ERROR 79

80 f(x) a μ x -σ-σσ-2σ-3σ2σ2σ3σ3σ 99.7% known as the confidence level (CL) x = µ ± 3σ QUANTIFYING RANDOM ERROR 80

81 Short-term Precision Analysis run at the same time by the same analyst using the same instrument and same chemicals Long-term Precision Compiled results over several months on a regular basis Repeatability Short-term precision under same operating conditions QUANTIFYING RANDOM ERROR 81

82 Reproducibility Ability of multiple laboratories to obtain same results on a given sample Ruggedness Degree of reproducibility of results by one laboratory under different conditions (long-term precision) Robustness (Reliability) Reliable accuracy and precision under small changes in condition QUANTIFYING RANDOM ERROR 82

83 CONFIDENCE LIMITS Refers to the extremes of the confidence interval (the range) Range of values within which there is a specified probability of finding the true mean (µ) at a given CL CL is an indicator of how close the sample mean lies to the population mean µ = x ± zσ 83

84 µ = x ± zσ If z = 1 we are 68.3% confident that x lies within ±σ of the true value If z = 2 we are 95.5% confident that x lies within ±2σ of the true value If z = 3 we are 99.7% confident that x lies within ±3σ of the true value CONFIDENCE LIMITS 84

85 s is not a good estimate of σ since insufficient replicates are made The student’s t-test is used to express CL The t-test is also used to compare results from different experiments - For N measurements CL for µ is CONFIDENCE LIMITS 85

86 That is, the range of confidence interval is – ts/√n below the mean and + ts/√n above the mean For better precision reduce confidence interval by increasing number of measurements CONFIDENCE LIMITS 86

87 To test for comparison of Means Calculate the pooled standard deviation (s pooled ) Calculate t Compare the calculated t to the value of t from the table The two results are significantly different if the calculated t is greater than the tabulated t at 95% confidence level (that is t cal > t tab at 95% CL) CONFIDENCE LIMITS 87

88 For two sets of data with - N 1 and N 2 measurements - standard deviations of s 1 and s 2 Degrees of freedom = N 1 + N 2 - 2 CONFIDENCE LIMITS 88

89 Using the t-test to Test for Systematic Error -A known valid method is used to determine µ for a known sample -- The new method is used to determine mean and standard deviation - t value is calculated for a given CL - Systematic error exists in the new method if t cal > t tab for the given CL CONFIDENCE LIMITS 89

90 F-TEST Used to compare two methods (method 1 and method 2) Determines if the two methods are statistically different in terms of precision The two variances (σ 1 2 and σ 2 2 ) are compared F-function = the ratio of the variances of the two sets of numbers 90

91 Ratio should be greater than 1 (i. e. σ 1 2 > σ 2 2 ) F values are found in tables (make use of two degrees of freedom) F cal > F tab implies there is a significant difference between the two methods F cal = calculated F value F tab = tabulated F value F-TEST 91

92 REJECTION OF RESULTS Outlier A replicate result that is out of the line A result that is far from other results Is either the highest value or the lowest value in a set of data There should be a justification for discarding the outlier The outlier is rejected if it is > ±4σ from the mean The outlier is not included in calculating the mean and standard deviation A new σ should be calculated that includes outlier if it is < ±4σ 92

93 REJECTION OF RESULTS Q – Test Used for small data sets 90% CL is typically used Arrange data in increasing order Calculate range = highest value – lowest value Calculate gap = |suspected value – nearest value| Calculate Q ratio = gap/range Reject outlier if Q cal > Q tab Q tables are available 93

94 Grubbs Test Used to determine whether an outlier should be rejected or retained - Calculate mean, standard deviation, and then G REJECTION OF RESULTS - Reject outlier if G cal > G tab - G tables are available 94

95 Performing Experiment 95

96 PERFORMING THE EXPERIMENT Detector Records the signal (change in the system that is related to the magnitude of the physical parameter being measured) Can measure physical, chemical or electrical changes Transducer (Sensor) Detector that converts nonelectrical signals to electrical signals and vice versa 96

97 Signals and Noise A detector makes measurements and detector response is converted to an electrical signal The electrical signal is related to the chemical or physical property being measured, which is related to the amount of analyte There should be no signal when no analyte is present Signals should be smooth but are practically not smooth due to noise PERFORMING THE EXPERIMENT 97

98 Signals and Noise Noise can originate from Power fluctuations Radio stations Electrical motors Building vibrations Other instruments nearby PERFORMING THE EXPERIMENT 98

99 Signals and Noise Signal-to-noise ratio (S/N) is a useful tool for comparing methods or instruments Noise is random and can be treated statistically Signal can be defined as the average value of measurements Noise can be defined as the standard deviation PERFORMING THE EXPERIMENT 99

100 Types of Noise 1. White Noise - Two types Thermal Noise Due to random motions of charge carriers (electrons) which result in voltage fluctuations Shot Noise When charge carriers cross a junction in an electrical circuit PERFORMING THE EXPERIMENT 100

101 Types of Noise 2. Drift (Flicker) Noise (origin is not well understood) 3. Noise due to surroundings (vibrations) Signal is enhanced or noise is reduced or both to increase S/N Hardware and software approaches are available Another approach is the use of Fourier Transform (FT) or Fast Fourier Transform (FFT) which discriminates signals from noise (FT-IR, FT-NMR, FT-MS) PERFORMING THE EXPERIMENT 101

102 Signals and Noise Signal has the information of the analyte Noise is the extraneous information in the information due to electronics, spurious response, and random events Signal to noise ratio –Noise is generally constant and independent of the signal –The impact of noise is greatest on the lowest signal The ratio of signal to noise is useful in evaluating data 102

103 Signal to Noise Value of the signal to noise can vary –Values less than 3 make it hard to detect signal

104 Sources of Noise Chemical Noise –Uncontrollable variables affecting chemistry of system under investigation Change in equilibria due to variations –Temperature –Pressure –Sample variation –Humidity 104

105 Signal to Noise Enhancement Hardware and software methods –Hardware is based on instrument design Filters, choppers, shields, detectors, modulators –Software allows data manipulation Grounding and Shielding –Absorb electromagnetic radiation Prevent transmission to the equipment –Protect circuit with conduction material and ground –Important for amplification 105

106 Hardware Difference and Instrumentation Amplifiers –Subtraction of noise from a circuit Controlled by a single resistor Second stage subtracts noise –Used for low level signal Analog filtering –Uses a filter circuit –Restricts frequency 106

107 Hardware Modulation –Changes low frequency signal to higher frequency Signal amplified, filter with a high pass filter, demodulation, low pass filter Signal Chopping –Input signal converted to square wave by electronic or mechanical chopper Square wave normalizes signal 107

108 Software Methods Ensemble Average –Average of spectra –Average can also be sum of collected spectra Boxcar average –Average of points in a spectra 108

109 Software Methods 109

110 Digital Filtering Numerical methods –Fourier transform Time collected data converted to frequency –NMR, IR –Least squares smoothing Similar to boxcar –Uses polynomial for fit –Correlation 110

111 Signals and Noise  Signal carries information about the analyte that is of interest to us.  Noise is made up of extraneous information that is unwanted because it degrades the accuracy and precision of an analysis  Signal-to-Noise Ratio S/N = (mean)/(Standard deviation) = Signal-to-noise (S/N) is much more useful figure of merit than noise alone for describing the quality of an analytical method. The magnitude of the noise is defined as the standard deviation s of numerous measurements and signal is given by the mean x of the measurements. S/N is the reciprocal of the relative standard deviation. S/N < 2 or 3  impossible to detect a signal. 111

112 Sources of Noise Analysis are affected by two types of noise: 1. Chemical noise 2. Instrumental noise Chemical noise: Arises from an uncontrollable variables that effect the chemistry of the system being analyzed. Examples are undetected variations in temperature, pressure, chemical equilibria, humidity, light intensity etc. 112

113 Instrumental Noise: Noise is associated with each component of an instrument – i.e., with the source, the input transducer, signal processing elements and output transducer. Noise is a complex composite that usually cannot be fully characterized. Certain kinds of instrumental noise are recognizable, such as: 1. Thermal or Johnson noise 2. Shot noise 3. Flicker or 1/f noise 4. Environmental noise 113

114 Instrumental Noise 1. Thermal Noise or Johnson Noise: Thermal noise is caused by the thermal agitation of electrons or other charge carriers in resistors, capacitors, radiation transducers, electrochemical cells and other resistive elements in an instruments. The magnitude of thermal noise is given by where, rms = root mean square noise,  f = frequency band width (Hz), k = Boltzmann constant (1.38 x 10 -23 J/K), T = temperature in Kelvin, R = resistance in ohms of the resistive element. Thermal noise can be decreased by narrowing the bandwidth, by lowering the electrical resistance and by lowering the temperature of instrument components. 114

115 Instrumental Noise 2. Shot Noise: Shot noise is encountered wherever electrons or other charged particles cross a junction. Where, i rms = root-mean-square current fluctuation, I = average direct current, e = charge on the electron (1.60 x 10 -19 C),  f = band width of frequencies. Shot noise in a current measurement can be minimized only by reducing bandwidth. 115

116 3. Flicker Noise: Flicker noise is characterized as having a magnitude that is inversely proportional to the frequency of the signal being observed. It is sometimes termed 1/f (one-over-f) noise. The cause of flicker noise are not well understood and is recognizable by its frequency dependence. Flicker noise becomes significant at frequency lower than about 100 Hz. Flicker noise can be reduced significantly by using wire-wound or metallic film resistors rather than the more common carbon composition type. 116

117 4. Environmental Noise: Environmental noise is a composite of different forms of noise that arise from the surroundings. Much environmental noise occurs because each conductor in an instrument is potentially an antenna capable of picking up electromagnetic radiation and converting it to an electrical signal. 117

118 Signal-to-Noise Enhancement: When the need for sensitivity and accuracy increased, the signal-to-noise ratio often becomes the limiting factor in the precision of a measurement. Both hardware and software methods are available for improving the signal-to-noise ratio of an instrumental method. 118

119 Hardware method: Hardware noise reduction is accomplished by incorporating into the instrument design components such as filters, choppers, shields, modulators, and synchronous detectors. These devices remove or attenuate the noise without affecting the analytical signal significantly. Hardware devices and techniques are as follows: 1.Grounding and Shielding: Noise that arises from environmentally generated electromagnetic radiation can be substantially reduce by shielding, grounding and minimizing the length of conductors within the instrumental system. 119

120 2. Analog Filtering: –By using low-pass and high-pass analog filters S/N ratio can be improved. –Thermal, shot and flicker noise can be reduced by using analog filters. 3. Modulation: –In this process, low frequency or dc signal from transducers are often converted to a higher frequency, where 1/f noise is less troublesome. –This process is called modulation. –After amplification the modulated signal can be freed from amplifier 1/f noise by filtering with a high- pass filter, demodulation and filtering with a low- pass filter then produce an amplified dc signal suitable for output. 120

121 4. Signal chopping: In this device, the input signal is converted to a square-wave form by an electronic or mechanical chopper. Chopping can be performed either on the physical quantity to be measured or on the electrical signal from the transducer. 121

122 5.Lock-in-Amplifiers: Lock-in-amplifiers permit the recovery of signals even when the S/N is unity or less. It requires a reference signal that has the same frequency and phase as the signal to be amplified. A lock-in amplifier is generally relatively free of noise because only those signals that are locked-in to the reference signal are amplified. All other frequencies are rejected by the system. 122

123 Software Method: Software methods are based upon various computer algorithms that permit extraction of signals from noisy data. Hardware convert the signal from analog to digital form which is then collected by computer equipped with a data acquisition module. Software programs are as follows: 1.Ensemble Averaging: In ensemble averaging, successive sets of data stored in memory as arrays are collected and summed point by point. After the collection and summation are complete, the data are averaged by dividing the sum for each point by the number of scans performed. The signal-to-noise ratio is proportional to the square root of the number of data collected. 123

124 124

125 2. Boxcar Averaging: Boxcar averaging is a digital procedure for smoothing irregularities and enhancing the signal-to-noise ratio. It is assumed that the analog analytical signal varies only slowly with time and the average of a small number of adjacent points is a better measure of the signal than any of the individual points. In practice 2 to 50 points are averaged to generate a final point. This averaging is performed by a computer in real time, i.e., as the data is being collected. Its utility is limited for complex signals that change rapidly as a function of time. 125

126 3. Digital filtering: Digital filtering can be accomplished by number of different well-characterized numerical procedure such as (a) Fourier transformation and (b) Least squares polynomial smoothing. (a)Fourier transformation: In this transformation, a signal which is acquired in the time domain, is converted to a frequency domain signal in which the independent variable is frequency rather than time. This transformation is accomplished mathematically on a computer by a very fast and efficient algorithm. The frequency domain signal is then multiplied by the frequency response of a digital low pass filter which remove frequency components. The inverse Fourier transform then recovers the filtered time domain spectrum. 126

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128 (b) Least squares polynomial data smoothing: This is very similar to the boxcar averaging. In this process first 5 data points are averaged and plotted. Then moved one point to the right and averaged. This process is repeated until all of the points except the last two are averaged to produce a new set of data points. The new curve should be somewhat less noisy than the original data. The signal-to-noise ratio of the data may be enhanced by increasing the width of the smoothing function or by smoothing the data multiple times. 128

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131 Calibration Curves 131

132 CALIBRATION CURVES Calibration The process of establishing the relationship between the measured signals and known concentrations of analyte Calibration standards: known concentrations of analyte Calibration standards at different concentrations are prepared and measured Magnitude of signals are plotted against concentration Equation relating signal and concentration is obtained and can be used to determine the concentration of unknown analyte after measuring its signal 132

133 Many calibration curves have a linear range with the relation equation in the form y = mx + b The method of least squares or the spreadsheet may be used m is the slope and b is the vertical (signal) intercept The slope is usually the sensitivity of the analytical method R = correlation coefficient (R 2 is between 0 and 1) Perfect fit of data (direct relation) if R 2 is closer to 1 CALIBRATION CURVES 133

134 BEST STRAIGHT LINE (METHOD OF LEAST SQUARES) The equation of a straight line y = mx + b m is the slope (  y/  x) b is the y-intercept (where the line crosses the y-axis) 134

135 BEST STRAIGHT LINE (METHOD OF LEAST SQUARES) The method of least squares finds the best straight line adjusts the line to minimize the vertical deviations Only vertical deviations are adjusted because experimental uncertainties in y values > in x values calculations for minimizing vertical deviations are easier 135

136 BEST STRAIGHT LINE (METHOD OF LEAST SQUARES) - N is the number of data points Knowing m and b, the equation of the best straight line can be determined and the best straight line can be constructed 136

137 Calibration of Instrumental Methods Analytical methods require calibration Process that relates the measured analytical signal to the concentration of analyte 3 common methods –Calibration curve –Standard addition method –Internal standard method 137

138 Calibration Curve Standards containing known concentrations of the analyte are introduced into the instrument Response is recorded Response is corrected for instrument output obtained with a blank –Blank contains all of the components of the original sample except for the analyte Resulting data are then plotted to give a graph of corrected instrument response vs. analyte concentration An equation is developed for the calibration curve by a least-squares technique so that sample concentrations can be computed directly 138

139 Standard Addition Method Usually involves adding one or more increments of a standard solution to sample aliquots of the same size (spiking) 139

140 Assessing the Data 140

141 ASSESSING THE DATA A good analytical method should be both accurate and precise reliable and robust It is not a good practice to extrapolate above the highest standard or below the lowest standard These regions may not be in the linear range Dilute higher concentrations and concentrate lower concentrations of analyte to bring them into the working range 141

142 ASSESSING THE DATA Limit of Detection (LOD) The lowest concentration of an analyte that can be detected Increasing concentration of analyte decreases signal due to noise Signal can no longer be distinguished from noise at a point LOD does not necessarily mean concentration can be measured and quantified 142

143 ASSESSING THE DATA Limit of Detection (LOD) Can be considered to be the concentration of analyte that gives a signal that is equal to 2 or 3 times the standard deviation of the blank Concentration at which S/N = 2 at 95% CL or S/N = 3 at 99% CL 3σ is more common and used by regulatory methods (e.g. EPA) 143

144 ASSESSING THE DATA Limit of Quantification (LOQ) The lowest concentration of an analyte in a sample that can be determined quantitatively with a given accuracy and precision Precision is poor at or near LOD LOQ is higher than LOD and has better precision LOQ is the concentration equivalent to S/N = 10/1 LOQ is also defined as 10 x σ blank 144

145 INSTRUMENTAL ANALYSIS 1) Electroanalytical Chemistry 2) Spectrochemical Analysis 3) Chromatographic Separations 145

146 A Typical Instrument Analytical Sample Signal Generator Signal Transducer Signal Processor i Output V 146

147 Types of Signals 1.Emission of Radiation 2.Absorption of Radiation 3.Scattering of Radiation 4.Refraction of Radiation 5.Diffraction of Radiation 6.Rotation of Radiation 7.Electrical Potential 8.Electrical Current 9.Electrical Resistance 10.Mass-to-charge Ratio 11.Reaction Rate 12.Thermal Properties 13.Mass 147

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