ADVANCED ANALYTICAL LAB TECH (Lecture) CHM

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1 ADVANCED ANALYTICAL LAB TECH (Lecture) CHM Spring 2015 Professor Andres D. Campiglia Textbook: Principles of Instrumental Analysis Skoog, Holler and Crouch, 5 th Edition, 6 th Edition or newest Edition 1

2 INTRODUCTION A common challenge faced by an analytical chemist is the determination of target species in complex samples Complex sample: sample with numerous species. Example of complex samples: physiological fluids (blood, urine, saliva), environmental samples (air, water, soil), etc. Target species is the species of interest. It is also called analyte. Example: benzo[a]pyrene in soil sample, PSA (prostate specific antigen) in physiological fluid, etc. Some possibilities: Analyte: Other species = concomitants: Analyte is the main component in the sample with only two types of species Analyte is not the main component in the sample but sample contains only two types of species Analyte is not the main component in the sample and sample contains several types of species 2

3 General Scheme Sample Collection Sample = Matrix Sample Preparation: Clean-up and/or Pre-concentration Analytical Sample Qualitative and Quantitative Analysis Statistical Analysis of Data 3

4 Quantitative and Qualitative Analysis Classical and instrumental methods Classical methods = wet-chemical methods Analyte separation: Qualitative analysis: precipitation, extraction or distillation chemical reactions yielding products of characteristic colors boiling or melting points solubility in a series of solvents odors, optical activities or refractive indexes Quantitative analysis: Gravimetric or volumetric analysis Main disadvantages of classical methods: Time consuming Numerous manual steps, which make them prone to indeterminate (random) errors 4

5 Instrumental Methods Most instrumental methods require a source of excitation to stimulate a measurable response from the analyte. See Figure 1-1. The first six entries in Table 1-1 involve interactions of the analyte with electromagnetic radiation. The first characteristic response involves radiant energy produced by the analyte. The next five properties involve changes in electromagnetic radiation brought about by its interaction with the sample. Four electrical properties and miscellaneous properties follow. The name of the corresponding instrumental method is given in the second column of Table

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7 Evaluation of Analytical Data (Appendix One) Analytical chemists may be presented with two types of problems 1) Provide a qualitative answer Example: Does this distilled water contain any Boron? Is this soil sample contaminated with polycyclic aromatic hydrocarbons (PAH)? 2) Provide a quantitative answer Example: How much lead is in this water sample? This steel sample contains traces of chromium, tungsten and manganese; how much of each one? Often, both types of questions are answered with quantitative methods Example: B, Pb, Cr, W, Mn in H 2 O: AAS or AES PAH in H 2 O: HPLC In cases where a positive answer is obtained, the analyst will give the answer in terms of analyte concentration Example: This water sample contain 1 mg/ml of B Most certainly, if the analyst repeats the experiment with the same sample using the same method he/she will find a different result Why? Because of inherent experimental errors 7

8 Random and systematic errors Example: Four students (A-D) each perform an analysis in which exactly 10.00mL of exactly 0.1M sodium hydroxide is titrated with exactly 10.00mL of exactly 0.1M hydrochloric acid. Each student performs five replicate titrations with the results shown in the following table Student Results (ml) A 10.08, 10.11, 10.09, 10.10, 10,12 B 9.88, 10,14, 10.02, 9.80, C 10.19, 9.79, 9.69, 10.05, 9.78 D 10.04, 9.98, 10.02, 9.97, A Results are all very close to each other ( ) = highly reproducible All the results are too high (they are all higher than 10.00, which is the theoretical value) Two separate types of errors have occurred with this student: Random errors: these cause the individual results to fall on both sides of the average value (10.10mL) Systematic errors: these cause all the results to be in error in the same sense (too high) Random errors affect the reproducibility of an experiment or precision Systematic errors affect the proximity of the experimental value to the theoretical value or accuracy 8

9 B The average of the five results (10.01mL) is very close to the theoretical value = data is accurate, without substantial systematic error The spread of the results is very large ( ) = data is imprecise, with the presence of substantial random errors Comparing A and B A: precise and inaccurate B: poor precision and accurate Random and systematic errors can occur independently of one another C His work is neither precise (range mL) nor accurate (average = 9.90mL) D Precise results ( mL) and accurate (average = 10.01mL) 9

10 Distinction between random and systematic errors, and precision and accuracy Student Results A Precise but inaccurate B Accurate but imprecise C Inaccurate and imprecise D Accurate and precise 10

11 Terms used to describe accuracy and precision of a set of replicate data Accuracy (systematic errors): absolute error or relative error #1 Precision (random errors): standard deviation, variance or coefficient of variation 11

12 Random Errors Whenever analytical measurements are repeated on the same sample, a distribution of data similar to that in Table a1-1 is obtained. The variations among the individual results are due to the presence of random (indeterminate) errors. The data can be organized into equal-sized, adjacent groups or cells, as shown in Table a1-2. Figure a1-1a shows the histogram of the data, i.e. the relative frequency of occurrence of results in each cell. As the number of measurements increases, the histogram approaches the shape of the continuous curve shown as plot B in Figure a1-1. Plot B shows a Gaussian curve, or normal error curve, which applies to an infinitely large set of data. Figure a1-1 Table a1-1 Table a1-2 12

13 Systematic Errors and the Gaussian Curve Systematic errors have a definite value and an assignable cause and are of the same magnitude for replicate measurements made in the same way. Systematic errors lead to bias in measurement results. Figure a1-2 shows the frequency distribution of replicate measurements in the analysis of identical samples by two methods that have random errors of identical size. Method A has no bias so that the mean (m A ) corresponds to the true value. Method B has a bias that is given by: Figure a1-2 bias = m B m A The analyst should be able to identify systematic errors and remove them from the method of analysis. 13

14 Statistical Treatment of Random Errors Random errors can not be completely eliminated from experiments. Statistical treatment of random errors provide the means to evaluate their contribution to final results. Definition of some terms: Population Mean (m) #2 Sample Mean #3 Population Standard Deviation (s) and Population Variance (s 2 ) #4 Sample Standard Deviation (s) and Sample Variance (s 2 ) #5 Relative Standard Deviation (RSD) and Coefficient of Variation (CV) #6 14

15 The Normal Error Law In Gaussian statistics, the results of replicate measurements arising from indeterminate (random) errors distribute according to the normal error law, which states that the fraction of a population of observations, dn/n, whose values lie in the region x to (x+dx) is given by: #7 The two plots in Figure a1-3a are plots of the equation above. The standard deviation for the data in curve B is twice that for the data in curve A. (x m) is the absolute deviation of the individual values of x from the mean. Figure a1-3b plots the deviations from the mean in terms of the variable z: z = x m / s when x m = s z = 1 x m = 2s z = 2 x m = 3s z = 3 and so forth. The distribution of dn/n in terms of the single variable z is given by: #8 Figure a1-3b Figure a1-3a 15

16 Characteristic Properties of the Normal Error Curve Zero deviation from the mean occurring with maximum frequency. Symmetrical distribution of positive and negative deviations about this maximum Exponential decrease in frequency as the magnitude of the deviation increases. Thus, small random errors are much more common than large random errors. The area under the curve in figure a1-3b is the integral of equation #8, which is given by: #9 The fraction of the population between any specified limits is given by the area under the curve between these limits. Examples: -1 z 1 DN/N = = 68.3% of a population of data lie within 1s. -2 z 2 DN/N = = 95.4% of a population of data lie within 2s. -3 z 3 DN/N = = 99.7% of a population of data lie within 3s. Figure a1-3b 16

17 Keep in mind the following: Confidence Intervals The equation for the Normal or Gaussian distribution is derived for a set of infinite measurements (N = ). Derivation assumes no systematic errors. The infinite number of measurements is called the population. The mean obtained with an infinite number of measurements is the true value (m). The true value has a standard deviation denoted by s. In practical situations the number of measurements is far from infinite. For a finite number of measurements, the set of results is called the sample. The mean (x) obtained with a sample is an estimate of the true (m) value and its standard deviation (s) is an estimate of s. In other words: when N ; x m and s s. In most of the situations encountered in chemical analysis, the true value of the mean (m) can not be determined because a huge number of measurements (N = infinite) would be required. The best we can do is to establish an interval surrounding an experimentally determined mean (x) within which the population mean (m) is expected to lie with certain degree of probability. This interval is known as the confidence interval. Example: assume an analysis for potassium gave concentration with the following confidence interval: % K. The significance of this result is the following: = = % probability that m is within this Interval of experimental results. 17

18 Calculation of Confidence Intervals When the value of s is known: The general expression of the confidence interval (CI) of the true mean of a set of measurements is obtained via the following equation: #10 Values of z at various confidence levels are given in Table a1-3. Note the following: a) For the same number of repetitions (N = constant) and as the probability increases, the size of the confidence interval increases with the value of z. b) For the same probability (z = constant), the size of the confidence interval decreases as the number of repetitions increases. When the value of s is unknown: When the number of repetitions is far from infinite (N 30), the confidence interval is calculated via the following equation: #11 Table a1-5 summaries t values for various levels of probability. With the t value the confidence interval follows the same trend as the one observed with the z value. 18

19 CALIBRATION OF INSTRUMENTAL METHODS (Chapter 1) Unless a correlation between the analyte response and the analyte concentration is somehow established by the analyst, Instrumentation by itself does not provide concentrations. A very important part of all analytical procedures is the calibration and standardization process. Calibration determines the relationship between the analytical response and the analyte concentration. Calibration is usually accomplished with the use of chemical standards. Two types of chemical standards: External standard is prepared separately from the sample. Internal standard is added to the sample itself. External standards are used when there is no interference effects from matrix components (concomitants) 19

20 The Calibration Curve Method The calibration curve method used when there is no interference effects from matrix components (concomitants). Experimental procedure for the calibration curve method: a) Several standards of known concentrations of analyte are introduced into the instrument and the instrumental response is recorded. b) The instrumental response is obtained with a blank. Blank = all the components of the analytical sample - analyte Analytical sample = is the sample presented to the instrument. In many cases, the analytical sample is different than the original sample. The signal intensity is plotted as a function of analyte concentration. If the relationship between signal and analyte concentration is linear, the perfect calibration curve should look as the one in the figure. The unknown concentration can then be obtained by interpolation. Analyte Concentration* Signal Zero I 0,1 ; I 0,2 ; I 0,3 I 0 ± s 0 C 1 I 1,1 ; I 1,2 ; I 1,3 I 1 ± s 1 C 2 I 2,1 ; I 2,2 ; I 2,3 I 2 ± s 2 C 3 I 3,1 ; I 3,2 ; I 3,3 I 3 ± s 3 C 4 I 4,1 ; I 4,2 ; I 4,3 I 4 ± s 4 Signal Average O = data points from external standards = data from unknown 20

21 You need to consider the following: The general behavior of experimental data is far from ideal This type of plot generates several questions: a) Is the calibration graph linear? b) What is the best straight line through these points? c) When the calibration plot is used for the analysis of a test sample, what are the errors and the confidence limits for the determined concentration? 21

22 Is the calibration graph linear? There are two ways of checking for linearity which are complementary rather than exclusive: Correlation coefficient Graphically Correlation coefficient The correlation coefficient (r) is given by the equation: #12 r can take values in the range 1 r 1 r = +1 describes perfect positive correlation, i.e. all the experimental points lie on a straight line of positive slope y r = -1 describes perfect negative correlation, i.e. all the experimental points lie on a straight line of negative slope r = 0 describes no linear correlation between y and x x 22

23 Example of calculation of r: Standard aqueous solutions of fluorescein are examined in a fluorescence spectrometer, and yield the following fluorescence intensities (in arbitrary units): Fluorescence intensity: Concentration, pg/ml:

24 Correlation coefficients are simple to calculate but they can lead to serious misinterpretation Keep in mind that the correlation coefficient equation will always generate an r value even if the data are patently non-linear in character, i. e. experience shows that even quite poor-looking calibration plots give very high r values Lesson of this example: Calibration curve must always be physically plotted On graph paper or computer monitor, otherwise a straight-line relationship might wrongly be deduced from the calculation of r This example is a remainder that r = 0 does not mean That y and x are entirely unrelated; it only means that they are not linearly related 24

25 Graphically Plot the data in a x versus y plot keeping always in mind the following convention: Analytical response = y Concentration of external standard = x Visually, determine the linear dynamic range (LDR): Calculate the correlation coefficient of the LDR excluding the data points that do not belong to the LDR. Include only the data points that belong to the LDR. Although you already know the graph is linear, the correlation coefficient gives you a quantitative measure on how well the data points fit a straight line. 25

26 What is the best straight line through these points? What points? The points that belong to the LDR. The points that you used to calculate the correlation coefficient. The mathematical expression that describes a straight line can be represented as: y = mx + b Where m is the slope and b is the intercept. y Experimental data points Blank signal b x 26

27 Random Errors in Concentrations Obtained with the Calibration Curve Method The least squares method assumes that any deviation of the individual points from the straight line arises from error in the measurement, i.e. only from the variation in the instrumental signal. In other words, the error in concentration is considered negligible in comparison to the instrumental signal. The difference between any given experimental value of the signal and the corresponding signal fitted in the best straight line by the least-squares method is called the residual. The concept is shown in figure a1-6. The least-squares method minimizes the residuals for all the experimental points to provide the best straight line within a given set of experimental data. The slope (m) of the best straight line is given by: #13 The intercept of the best straight line is given by: #14 The standard deviation of the slope (s m ) is given by: #15 The standard deviation of the intercept (s b ) is given by: #16 The standard deviation of a concentration (s c ) is given by: #17 Confidence interval is given by: #18 27

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29 Standard-Addition Methods Standard addition methods are particularly useful for analyzing complex samples in which the likelihood of matrix effects is substantial. One of the most common standard addition procedures involves adding one or more increments of a standard solution to sample aliquots containing identical volumes. Each solution is then diluted to a fixed volume before measurement. Assume that several aliquots Vx of the unknown solution with an unknown concentration Cx are transferred to volumetric flasks having a volume V t. To each of these flasks is added a variable volume Vs of a standard solution of the analyte having a known concentration Cs. Suitable reagents are added and each solution is diluted to volume. Instrument measurements are then made on each of these solutions and corrected for any blanks response to yield a net instrument response S. Assuming that the blank-corrected instrument response is proportional to analyte concentration: S = kvscs / V t + kvxcx/v t Where k is a proportionality constant. A plot of S as a function of Vs is a straight line where the slope m and the intercept b are given by: m = kcs/v t and b = kvxcx/v t 29

30 Volumetric flask 1 with volume V t Volumetric flask 2 with volume V t Volumetric flask 3 with volume V t Volumetric flask 4 with volume V t Volumetric flask 5 with volume V t Add the same volume of solution (Vx) of unknown concentration (Cx) of to the five volumetric flasks Volumetric flask 1 with analyte mass = CxVx Volumetric flask 2 with analyte mass = CxVx Volumetric flask 3 with analyte mass = CxVx Volumetric flask 4 with analyte mass = CxVx Volumetric flask 5 with analyte mass = CxVx To each of these flasks is added a variable volume Vs of a standard solution of the analyte having a known concentration Cs No standard addition Standard Volume = Vs Analyte mass = CsVs Standard Volume = 2Vs Analyte mass = 2CsVs Standard Volume=3Vs Analyte mass = 3CsVs Standard Volume=4Vs Analyte mass = 4CsVs Volumetric flask 1 with analyte mass = CxVx Volumetric flask 2 with analyte mass = CxVx Volumetric flask 3 with analyte mass = CxVx Volumetric flask 4 with analyte mass = CxVx Volumetric flask 5 with analyte mass = CxVx 30

31 Volumetric flask 1 with analyte mass = CxVx + 0CsVs Volumetric flask 2 with analyte mass = CxVx + CsVs Volumetric flask 3 with analyte mass = CxVx + 2CsVs Volumetric flask 4 with analyte mass = CxVx + 3CsVs Volumetric flask 5 with analyte mass = CxVx + 4CsVs Suitable reagents are added and each solution is diluted to volume Volumetric flask 1 with CxVx + 0CsVs + reagents + solvent Volumetric flask 2 with CxVx + CsVs + reagents + solvent Volumetric flask 3 with CxVx + 2CsVs + reagents + solvent Volumetric flask 4 with CxVx + 3CsVs + reagent + solvent Volumetric flask 5 with CxVx + 4CsVs + reagent + solvent General formula that represents analyte concentration (C A ) in any given volumetric flask: C A = CxVx + ncsvs / V t where n = 0, 1, 2, 3, 4, If we make nvs = Vs C A = CxVx + CsVs / V t ; where Vs is the variable volume of standard addition 31

32 Instrument measurements are then made on each of these solutions and corrected for any blanks response to yield a net instrument response S S 0 - S blank S 1 - S blank S 2 - S blank S 3 - S blank S 4 - S blank Volumetric flask 1 with CxVx + CsVs + reagents + solvent Volumetric flask 2 with CxVx + CsVs + reagents + solvent Volumetric flask 3 with CxVx + CsVs + reagents + solvent Volumetric flask 4 with CxVx + CsVs + reagent + solvent Volumetric flask 5 with CxVx + CsVs + reagent + solvent Assuming that the blank-corrected instrument response is proportional to analyte concentration: S = kvscs / V t + kvxcx/v t ; where k is a proportionality constant 32

33 The analytical signal is plotted vs. the volume of standard added to the volumetric flasks: S Volume of standard equivalent to the amount of analyte present in the unknown sample. Best straight line obtained by the least square method Y = mx + b Vs m = kc s / V t and b = kv x C x / V t b / m = kv x C x /V t = V x C x or C x = bc s / mv x KC s /V t C s 33

34 The standard deviation in concentration is given by: #19 The standard deviation in volume is given by the following equation: #20 34

35 The standard addition is a powerful calibration method that is often used improperly due to failure to understand the assumptions involved There must be a good blank measurement so that there is no contribution to the measured analytical signal from other species Curve a is obtained with a proper blank measurement while in curve b the blank measurement does not compensate for a blank interference, so all analytical signals are too high by a fixed amount, and the value of Cx determined is too high The calibration curve for the analyte in the sample matrix must be linear Note: The multiple addition procedure provides a check of this assumption Analyte interferences must increase or decrease the analytical signal from the original analyte in the sample and the analyte added in the addition by the same constant fraction independent of analyte concentration The standard addition procedure provides a check on recovery and the presence of analyte interferences. The slope of a standard additions plot can be compared to the slope of a conventional calibration curve. If the slopes are different, the recovery of the analyte is incomplete or analyte interferences in the sample matrix affect the slope 35

36 Exercise Modified Exactly 5.00 ml aliquots of a solution containing phenobarbital were measured into ml volumetric flasks and made basic with KOH. The following volumes of standard solution of phenobarbital containing mg/ml of phenobarbital were then introduced to each flask and the mixture was diluted to volume: 0.000, 0.500, 1.00, 1.50, and 2.00 ml. The fluorescence of each of these solutions was measured with a fluorimeter, which gave values of 0.326, 4.80, 6.41, 8.02, and 9.56 counts per second (cps), respectively. The blank signal was equal to 1.00 cps. a) Come up with the composition of a suitable blank. b) Plot the data. c) Using the plot from (b), calculate the concentration of phenobarbital in the unknown. d) Derive a least-squares equation for the data. e) Find the concentration of phenobarbital from the equation (d). f) Calculate a standard deviation for the concentration obtained in (d). 36

37 Example

38 Analytical Figures of Merit (AFOM) Linear Dynamic Range (LDR) Limit of Quantitation Limit of Detection Sensitivity Analytical Sensitivity Relative Standard Deviation 38

39 Linear Dynamic Range (LDR) or Dynamic Range, Limit of Quantitation (LOQ) and Limit of Detection The LDR of an analytical method extends from the lowest concentration at which quantitative measurements can be made (limit of quantitation, LOQ) to the concentration at which the calibration curve departs from linearity (limit of linearity, LOL). LOQ is the signal equivalent to 10 times the standard deviation of the blank. LDRs are usually expressed in terms of orders of magnitude. The limit od detection (LOD) is defined as the minimum concentration or mass of analyte that can be detected at a known confidence level. 39

40 Sensitivity and Selectivity Sensitivity is the ability of a method to discriminate between small differences in analyte concentrations. Two parameters limit sensitivity: the slope of the calibration curve and the precision of measurements. There are two figures of merit for sensitivity: calibration sensitivity and analytical sensitivity. Selectivity of an analytical method refers to the ability of the method to accurately determine the analyte in the presence of concomitants. Concomitants can cause spectral interference, chemical interference or both. 40

41 Introduction to Spectroscopy (Chapter 6) Electromagnetic radiation Sample Spectrum Before even attempting to understand spectrochemical analysis, one needs to have a basic understanding of electromagnetic radiation and radiation and matter interactions How is electromagnetic radiation generated? How is electromagnetic radiation detected? How is a spectrum generated? Before even attempting to understand spectrochemical analysis, one needs to have a basic understanding of instrumentation 41

42 Electromagnetic radiation Electromagnetic radiation can be described by two models: the wave model and the particle model. The two models are not exclusive but, rather, complementary. Wave properties of electromagnetic (EM) radiation An EM wave can be represented as electric and magnetic fields that undergo in-phase sinusoidall oscillations at right angles to each other and to the direction of propagation. Both fields can be represented as vectors perpendicular to each other and to the direction of propagation Wave of EM radiation Polarizer Plane-polarized EM radiation The term plane-polarized implies that all oscillations of either the electric or the magnetic fields lie within a single plane Plane-polarized EM radiation Wavelength selector Monochromatic plane-polarized radiation The term monochromatic implies that the EM radiation is composed only by one wavelength 42

43 Representation of a beam of monochromatic, plane-polarized radiation: Interaction of the electric field and the magnetic field of an EM wave on an orbit about the nucleus We will focus our discussion on the electric field of the EM wave 43

44 Velocity = wavelength x frequency 44

45 Some important properties of EM waves One of the most interesting characteristics of light is that no matter what its color or frequency, the wavelength times the frequency is a constant that we know as the speed of light. The frequency of the EM radiation is determined by the source and remains constant, i.e. it does not depend on the medium of propagation (air, water, vacuum, glass, etc.). The velocity of propagation of a wave depends on the composition of a medium. If the velocity of propagation depends on the medium, so does the wavelength. Refractive index Refraction of radiation Reflection of radiation 45

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47 The Electromagnetic Spectrum Interactions of Radiation with Matter Absorption and emission spectra 47

48 Absorption of Radiation Example: Atomic absorption spectroscopy Instrumentation 48

49 Emission of Radiation Example: Atomic Emission Spectroscopy Instrumentation 49

50 Spectral differences between atoms and molecules Absorption of radiation 50

51 Spectral differences between atoms and molecules Emission of radiation 51

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54 Multiplicity of an electronic state The multiplicity (M) of an electronic state is related to the total spin quantum number, i.e.: M = 2S + 1 The total spin quantum number is equal to: S = s i, where s i = +1/2 or -1/2. Molecules in the ground state have a total spin quantum number equal to zero. As a consequence, the multiplicity of the ground state is equal to 1. Electronic states with multiplicity equal to 1 are called singlet states and denoted by S. When one of the two electrons of opposite spins, belonging to a molecular orbital of a molecule in the ground state, is promoted to a molecular orbital of higher energy, its spin is - in general - unchanged. Because the total spin quantum number does not change, the multiplicity of the ground and excited state do not change and the transition is called a singlet-singlet transition: S 0 S 1 ; S 0 S 2 ; S 1 S 2 ; etc. S 0 denotes the ground state. A molecule in the singlet state may undergo a state where the promoted electron has changed its spin; because there are then two electrons with parallel spins, the total spin quantum number is 1 and the multiplicity is 3. Such a state is called a triplet state (T 1, T 2, T 3, etc.) and the transition is called singlet-triplet transition. 54

55 Example of Electronic Transitions in a Molecule Energy levels of molecular orbitals in formaldehyde HOMO: Highest Occupied Molecular Orbital LUMO: Lowest Unoccupied Molecular Orbital 55

56 Photoluminescence Phenomena S = Singlet electronic states S 0 = fundamental electronic state = ground state S 1 = first singlet excited state S 2 = second singlet excited state T = Triplet electronic states T 2 = second triplet excited state T 1 = first triplet excited state Vibrational levels are associated with each electronic state Rotational levels are not represented in the diagram Radiationless processes: IC = internal conversion ISC = intersystem crossing VR = vibrational relaxation Emitting processes: Fluorescence Phosphorescence Delayed ( Late ) Fluorescence: not represented 56

57 Optical Spectroscopy Methods are based on the Absorption of Radiation Absorption of radiation is related to Transmittance 57

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59 Chapter 7 (a) Molecular absorption spectroscopy (b) Molecular fluorescence spectroscopy (c) Atomic emission spectroscopy 59

60 Excitation sources Conventional sources Laser sources Conventional Sources a) Spectral output b) Temporal behavior a) Spectral output Continuum sources Line sources Continuum plus line b) Temporal behavior Continuous Pulsed 60

61 Continuum sources Emit a continuum spectrum over a broadband wavelength region There are two types: Incandescent lamps See examples a and b They are basically a resistive material heated electrically. As current passes through the resistance, temperature raises and part of the energy is dissipated in the form of light Arc discharge lamps See examples c to e These lamps are quartz or glass envelopes containing a gas that, upon plasma formation, emit radiation 61

62 Incandescent lamps The spectral radiance of an incandescent lamp follows a theoretical model known as blackbody A blackbody absorbs all radiant energy upon it regardless wavelength. I has unity spectral absorbance at all wavelengths and emits as much energy as it absorbs The spectral radiance of a blackbody is given by the following equation: where: B l b = spectral radiance of the blackbody in W. cm -2.sr -1.nm -1 h = Plank s constant = x Js k = Boltzmann s constant = x J K -1 c = 3 x 10 8 m.s -1 T = temperature (K) l = wavelength of emission (nm) c 1 = 2hc 2 = x W.nm 4.cm -2.sr -1 c 2 = hc/k = x 10 7 nm K 62

63 From the equations we note that the spectral radiance at a given wavelength depends only on temperature The figure shows a plot of B l b vs. l at several temperatures. Note the wavelength shift to the blue and the increase in the spectral radiance as the temperature increases The wavelength of maximum radiance (l m ) is obtained by differentiating the spectral radiance equation with respect to wavelength and setting the derivative equal to zero where: l is in nm and T is in K 63

64 To describe the spectral radiance of real sources, often called gray bodies, the spectral radiance equation of the blackbody model needs to be modified to account for non-idealities where: e (l) = spectral emissivity of the source T w (l) = transmission factor of the lamp window 0 < e (l) < 1 e (l) is the ratio of the spectral radiance of the real source to that of the blackbody at a specific wavelength and temperature #T w (l) accounts for reflective losses and absorptions at the window surface of the lamp if the lamp is enclosed in an envelope such as quartz or glass. In cases where there is no envelope, T w (l) = 1 The figure compares the total emittance of a blackbody and a tungsten lamp 64

65 Arc lamps Arc lamps consist of a sealed glass or quartz envelope filled with a gas The two electrodes (cathode and anode) initiate a discharge in the envelope that is maintained by a dc or ac current The discharge creates electrons at the cathode that are accelerated towards the anode Gas AC or DC Collisions between the electrons and gas cause ionization of gas molecules = electron Positive ions are accelerated towards the cathode. Upon collision with the cathode, positive ions produce secondary electrons Cathode (-) Anode (+) Secondary electrons collide with gaseous molecules to maintain ionization in the tube. A plasma is created that emits radiation Cathode (-) Anode (+) = positive ion 65

66 Hydrogen and deuterium lamps provide strong spectral continua in the UV spectral region At wavelengths longer than 370 nm, the spectra from hydrogen and deuterium are no longer continua In the visible region, the spectral radiance of hydrogen or deuterium lamps is rather weak Spectrophotometers that operate in the UV and visible regions often require two sources: a hydrogen or deuterium lamp is used for the UV region ( nm), and a tungsten-filament lamp is used for the visible region (350 nm) Spectral irradiance of a D 2 lamp Molecular fluorescence and phosphorescence spectrometry require high-intensity, continuum sources of UV and visible radiation. The Xe arc lamp is the most common source for molecular luminescence spectrometry The Xe-Hg lamp is an example of a continuum + line source. The spectral radiance is high, exceeding 1 W cm -2 nm -1 sr -1. Because of the presence of atomic lines, this source is not very useful for molecular absorption spectroscopy, where it is desirable to have a flat spectral distribution. It is an excellent source for photoluminescence spectroscopy, mainly if a Hg line corresponds to the wavelength of excitation of the compound of interest (a) (b) Spectral radiance of a Xe lamp Spectral radiance of a Xe-Hg lamp 66

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68 The following table summaries several characteristics of common continuum sources Note the following: a) Nernst glower and Globar are IR sources. Their intensity is much weaker than UV and visible sources b) Tungsten lamps emit stronger in the visible than H 2 or D 2 lamps c) Xe lamps emit strongly in the ultraviolet and visible regions 68

69 Wavelength selectors There are three types: filters, monochromators and spectrographs Filters There are four common types: band-pass or absorption filters, cut-off filters, density filters and interference or Fabry-Perot filters Band-pass, cut-off and density filters are based on the absorption of radiation Incident Radiation Io Transmitted Radiation I A = - log T = - log I/Io A = absorbance T = transmittance Filter made of absorbing material Absorbing materials can be colored glasses, crystals, solutions, thin films, etc. Wavelength selection is usually achieved with absorption or interference filters. 69

70 Band-pass filters Band-pass filters are characterized by plots of their spectral transmittance vs. wavelength. The characteristics of interest are shown in the first figure: l m = wavelength of maximum transmittance T m Dl = full-width at half maximum (FWHM) l m and Dl depend on the absorbing material, as shown in the second and third figure Typical values of the FWHM range from 30 to 250 nm Examples of their use in analytical spectroscopy a) photometers Transmittance of Corning glass filters. The numerical designations are the product numbers for specific filters. 70

71 Interference filters The first figure shows a Fabry-Perot interference filter The thin dielectric is a material of low refractive index such as quartz, CaF 2, MgF 2, ZnS, ThF 4, or sapphire The filter is constructed in such a way that the rays from most wavelengths that strike the filter suffer destructive interference, while only rays within a small wavelength band experience constructive interference and are passed The condition for constructive interference is where: d = dielectric thickness h = refractive index of dielectric material q = angle of incidence n = order = 1,2,3, l = transmitted wavelength (a) (b) Schematic cross-section of interference filter Schematics to show conditions for constructive interference 71

72 Echellette Grating nl = d(sini + sinr) 72

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74 Dispersion Angular dispersion: dr/dl = n/dcosr Linear dispersion: D = dy/dl = f (dr/dl) Reciprocal linear dispersion: D -1 = dl/dy = (1/f)(dl/dr) D -1 = dcosr/nf Units of D -1 in UV-Vis nm/mm or Å/mm At small angles of diffraction (r<20 ): cosr 1 D -1 = d/nf For small angles of diffraction the linear dispersion of a monochormator is constant. 74

75 Resolving Power of a Monochromator It describes the limit of a monochromator to separate adjacent images that have a slight difference in wavelengths R = l / Dl Where: l = average wavelength of the two images Dl = difference between the two wavelengths R = l / Dl = nn Where: n = diffraction order N = number of grating blazes illuminated by radiation from the entrance slit Better resolution is a characteristic of longer gratings, smaller blaze spacing's, and higher diffraction orders Light Gathering Power of Monochromators Also known as the f-number (F) of a monochromator It provides a measure of the ability of a monochromator to collect the radiation that emerges from the entrance slit F = f/d where: f = focal length of the collimating mirror (or lens) and d is the diameter The light-gathering power of an optical device increases as the inverse square of the f- number => f/2 lens gathers 4x more light than f/4 lens Typical R values for bench-top UV-Vis monochromators = 10 3 to

76 Echelle Grating Echelle gratings are used in Echelle monochromators Echelle monochromators contain two dispersing elements arranged in series r i = b nl = 2dsinb D -1 = dcosb / nf High dispersion is achieved by making the angle b small and the order of diffraction n large 76

77 For the same focal length, the linear dispersion and resolution are an order of magnitude greater for the echelle The light-gathering power of the echelle is also somehow superior Echelle gratings are very common in Atomic Emission Spectroscopy 77

78 Fig Bandwidth: span of monochromator settings needed to move the image of the entrance slit across the exit slit Effective bandwidth or spectral bandpass or spectral slit width: one-half of the bandwidth when the two slits (entrance and exit) are identical Dl eff = wd -1 78

79 Choice of Slits Most monochromators are equipped with variable silts so that the effective bandwidth can be changed. The use of the minimal slit width is desirable when narrow absorption or emission bands must be resolved. The available rediant power decreases significantly when the slits are narrowed: Molecular spectroscopy (I a w 2 ) Atomic spectroscopy (I a w) Wider slit widths may be used for quantitative analysis rather than for qualitative analysis. 79

80 Optical transducers The purpose of an optical transducer is to convert radiant power into an electrical signal Optical transducers fall into two categories: a) Thermal detectors b) Photon detectors Thermal detectors sense the change in temperature that is produced by the absorption of incident radiation Photon detectors respond to incident photon arrival rates rather than to photon energies 80

81 Photon detector characteristics The following characteristics are useful to compare photon detectors: a) Responsivity b) Linear range c) Spectral responsivity Responsivity and linear range Spectral responsivity 81

82 Vacuum phototube The cathode is a photosensitive material such as Cs 3 Sb or AgOCs. When photons of a certain energy strike the photosensitive material, electrons are ejected from the cathode. Only photons with greater than threshold energy yield photoelectrons with sufficient kinetic energy to escape the photocathode. The electrons ejected from the photocathode are attracted by the anode, which is positively biased in relation to the cathode. The electron flux leaving the cathode is known as the cathodic current. Only a fraction of cathodic electrons are collected at the anode. The electrons arriving at the anode create the anodic current that is measured with an external circuit. 82

83 Photomultiplier Tube The PMT contains a photosensitive cathode (photocathode) and a collection anode The cathode and the anode are separated by several electrodes (dynodes) that provide electron multiplication or gain The cathode is biased negative with respect to the anode (the potential difference is anywhere from 400 to 2500V) A photoelectron ejected by the photocathode strikes the first dynode and releases 2 to 5 secondary electrons Each secondary electron is accelerated by the electric field between the first and second dynode with sufficient energy to release another 2 to 5 electrons in the second dynode Since each dynode down the chain is biased 100V more positive than the preceding dynode, this multiplication process continues until the pulse of electrons reach the anode 83

84 Photodiodes P-n junction A photodiode detector is a p-n junction operating in a reverse-bias mode Absorption of EM radiation by the p-n junction causes covalent bonds to brake forming hole-electron pairs that populate the depletion region Since the number of hole-electron pairs in the depletion region increases with the arrival of photons, the limiting current is proportional to the radiant power of incident radiation The voltage drop across a load resistor is measured and the voltage is proportional to the arrival of photons ate the depletion zone 84

85 N-semiconductor Silicon (IVA) is doped with trace quantities of P (VA). The free electron of P is free to move along the Si lattice P-semiconductor Silicon (IVA) is doped with trace quantities of B (IIIA). The lack of an electron creates a hole that electrons can migrate from Si to B. Electron migration creates positive charges

86 The photodiode is a p-n junction under reverse bias Negative terminal Positive terminal 86

87 PN junction reverse biased: Initially, there is a very small amount of current because of the minority of carriers crossing the junction. The combination of electrons and holes creates a depletion region with negligible charge. The depletion region acts as a barrier for further attempts of charges crossing the barrier. High resistance to current flow. 87

88 Forward Biased Conduction When the p-n junction is forward biased, the electrons in then-type material combine with the holes in the p-type material, making possible a continuous forward current through the junction. Low resistance to current flow. 88

89 Linear photodiode array (LPDA) LPDA is a linear arrangement of several small silicon photodiodes The typical dimension of each element (pixel) is 2.5 by mm The number of transducers in a chip ranges from 64 to 4096, with 1024 being perhaps the most widely used The LPDA is operated in the charge storage mode. The charge accumulated by each element is given by: Where: q = accumulated charge (C) E = incident radiation (W) R(l) = responsivity (A.W -1 ) t = integration time (s) Note: longer integration times accumulate more charge and provide better signal-tonoise ratios 89

90 How does it work? The LPDA is placed at the focal plane of the exit slit of a monochromator (spectrograph) Photodiodes located at different positions in the linear array are exposed to different wavelengths Each pixel, or set of pixels, collects the intensity at a specific wavelength The computer screen plots intensity versus wavelength. The wavelength corresponding to each pixel is known because the multi-channel system is calibrated taking into consideration the optical parameters of the spectrograph and the dimensions of the LPDA Obtaining a scan with the LPDA corresponds to the process of sequential pixel interrogation. See figure To interrogate the entire array takes a period of microseconds. The longer the interrogation time, the longer it takes to obtain a scan 90

91 The first figure shows the stored signal charge as a function of light exposure for a Silicon LPDA at a wavelength of 575 nm The charge accumulates linearly until reaching the saturation charge where the corresponding exposure is the saturation exposure The second figure shows the responsivity of the LPDA. The responsivity is defined as the ratio between the saturation charge and the saturation exposure LPDA can not match the performance PMT with respect to sensitivity, dynamic range and signal-to-noise ratio 91

92 Charge-coupled device (CCD) CCDs are silicon-based semiconductor chips bearing two dimensional matrixes of photodiodes or pixels The pixels are arranged in rows and columns. Rows run horizontally and columns vertically. See figure A typical CCD chip may comprise 256 rows and 1024 columns When the CCD is placed at the focal plane of a spectrograph, the position of a pixel (or several pixels) corresponds to the position of a projected wavelength image. The charge collected by that pixel (or set of pixels) corresponds to the intensity of radiation at that wavelength 92

93 TYPES OF OPTICAL INSTRUMENTS It is a rarity that all the optical information produced in a spectrochemical measurement is useful or desirable. Sorting out the desirable optical information is a major step in a spectrochemical measurement. The vast majority of optical spectroscopic techniques select the desired information based on its wavelength. Wavelength selection in spectrochemical measurements can be based on absorption or interference filters, spatial dispersion of wavelengths or interferometry. Wavelength selectors which disperse the spectral components of the optical signal spatially are the most common. Some of the major configurations are shown in the figure below: => The entrance slit defines the area of the source of radiation that is viewed. => The dispersive element can be a prism which spatially separate wavelengths by refraction or a grating that disperses light based on diffraction. => The image transfer system produces an image of the entrance slit on the focal plane. The name of the wavelength selector depends on the arrangement of apertures or slits in the focal plane where the spectrum is dispersed: => Spectrograph => Monochromator => Polychromator 93

94 The name of the instrument depends on both the wavelength selector and the type of detection system Spectroscope: is an optical instrument used for the visual identification of atomic emission lines. It uses a spectrograph with a viewing screen for observing the spectrum in the focal plane. Colorimeter: is an instrument for absorption measurements in which the human eye serves as the detector using one or more color-comparison standards. Photometer: consists of a source, a filter, a photoelectric transducer, and a signal processor and readout system. Fluorometer or fluorimeter: photometers designed for fluorescence measurements. Spectrometer: is an instrument that provides information about intensity of radiation as a function of wavelength or frequency. Dispersing unit can be a monochromator, a spectrograph or a polychromator. Spectrophotometer: is a spectrometer equipped with one or more exit slits and photoelectric transducers. Spectrofluorometer or spectrofluorimeter: spectrophotometer for fluorescence analysis. Single-channel and multi-channel spectrometers Fig UV-Vis Absorption Spectrophotometer for molecular spectroscopy 94

95 Phototubes, PMT and photodiodes are used in single channel spectrometers for both atomic and molecular spectroscopy Fig a Single-channel system for UV-Vis molecular absorption spectroscopy Fig. 9-13a Single-channel system for Atomic Absorption Spectroscopy (AAS) 95

96 LPDA, CCD and CID are used in multiple-channel spectrometers for both atomic and molecular spectroscopy Multi-channel system for UV-Vis molecular absorption spectroscopy Fig Fig Multi-channel system for Atomic Emission Spectroscopy (AES) 96

97 INTRODUCTION TO OPTICAL ATOMIC SPECTROSCOPY Atomic spectroscopy techniques: Optical spectrometry Mass spectrometry X-Ray spectrometry Optical spectrometry: Elements in the sample are atomized before analysis. Atomization: Elements present in the sample are converted to gaseous atoms or elementary ions. It occurs in the atomizer (see Table 8-1). Optical spectroscopy techniques: Atomic Absorption Spectroscopy (AAS) Atomic Emission spectroscopy (AES) Atomic Fluorescence Spectroscopy (AFS) 97

98 Optical Atomic Spectra Figure 8-1a shows the energy level diagram for sodium. A value of zero electron volts (ev) is arbitrarily assigned to orbital 3s. The scale extends up to 5.14eV, the energy required to remove the single 3s electron to produce a sodium ion. 5.14eV is the ionization energy. A horizontal line represents the energy of and atomic orbital. p orbitals are split into two levels which differ slightly in energy: 3s 3p: l = 5896Å or 5890Å 3s 4p: l = 3303Å or 3302Å 3s 5p: l = Å or Å There are similar differences in the d and f orbitals, but their magnitudes are usually so small that are undetectable, thus only a single level is shown for orbitals d. Spin-orbit coupling 98

99 Multiplicity: number of possible orientations of the resultant spin angular momentum = 2S +1 99

100 Atomic Line Widths Widths of atomic lines are quite important in atomic spectroscopy. Narrow lines in atomic and emission spectra reduce the possibility of interference due to overlapping lines. Atomic absorption and emission lines consists of a symmetric distribution of wavelengths that centers on a mean wavelength (l 0 ) which is the wavelength of maximum absorption or maximum intensity for emitted radiation. The energy associated with l 0 is equal to the exact energy difference between two quantum states responsible for absorption or emission. A transition between two discrete, singlevalued energy states should be a line with line-width equal to zero. However, several phenomena cause line broadening in such a way that all atomic lines have finite widths. Line width or effective line width (Dl 1/2 ) of an atomic absorption or emission line is defined as its width in wavelength units when measured at one half the maximum signal. Sources of broadening: (1) Uncertainty effect (2) Doppler effect (3) Pressure effects due to collisions (4) Electric and magnetic field effects 100

101 Uncertainty Effect It results from the uncertainty principle postulated in 1927 by Werner Heisenberg. One of several ways of formulating the Heisenberg uncertainty principle is shown in the following equation: Dt x DE = h The meaning in words of this equation is as follows: if the energy E of a particle or system of particles photons, electrons, neutrons or protons is measured for an exactly known period of time Dt, then this energy is uncertain by at least h/ Dt. Note: Dl = Dl 1/2 Therefore, the energy of a particle can be known with zero uncertainty only if it is observed for an infinite period of time. For finite periods, the energy measurement can never be more precise then h/ Dt. The lifetime of a ground state is typically long, but the lifetimes of excited states are generally short, typically 10-7 to 10-8 seconds. Line widths due to uncertainty broadening are called natural line widths and are generally 10-5 nm or 10-4 Å. 101

102 Doppler Effect In a collection of atoms in a hot environment, such as an atomizer, atomic motions occur in every direction. The magnitude of the Doppler shift increases with the velocity at which the emitting or absorbing species approaches or recedes the detector. For relatively low velocities, the relationship between the Doppler shift (Dl) and the velocity (v) of an approaching or receding atom is given by: Dl / l 0 = v / c Where l 0 is the wavelength of an un-shifted line of a sample of an element at rest relative to the transducer, and c is the speed of light. Dl Emitting atom moving: (a) towards a photon detector, the detector sees wave crests more often and detect radiation of higher frequency; (b) away from the detector, the detector sees wave crests less frequently and detects radiation at lower frequency. The result is an statistical distribution of frequencies and thus a broadening of spectral lines. 102

103 Pressure Effects Due to Collisions Pressure or collisional broadening is caused by collisions of the emitting or absorbing species with other atoms or ions in the heated medium. These collisions produce small changes in energy levels and hence a range of absorbed or emitted wavelengths. Energy (ev) E 2 E 1 l A l E l A l E Atom 1 Atom 2 E 2 E 1 These collisions produce broadening that is two to three orders of magnitude grater than the natural line widths. Example: Hollow-cathode lamps (HCL): Pressure in these lamps is kept really low to minimize collisional broadening. Glass tube is filled with neon or argon at a pressure of 1 to 5 torr. 103

104 The Effect of Temperature on Atomic Spectra Temperature in the atomizer has a profound effect on the ratio between the number of excited an unexcited atomic particles. The magnitude of this effect is calculated with the Boltzmann distribution equation: N j / N 0 = (g j / g 0 ) x [exp(-e j /kt)] where: - N j and N 0 are the number of atoms in the excited state and ground state, respectively - k is the Boltzmann s constant - T is absolute temperature (K) - E j is the energy difference between the excited and the ground state. - g i and g 0 are statistical factors called statistical weights determined by the number of states having equal energy at each quantum level. Example shows that a temperature fluctuation of only 10K results in a 4% increase in the number of excited sodium atoms. A corresponding increase in emitted power by the two lines would result. An analytical method based on the measurement of emission requires close control of atomization temperature. 104

105 Band and Continuum Spectra Associated with Atomic Spectra When atomic line spectra are generated, both band and continuum radiation are usually produced as well. Molecular bands often appear as a result of molecular species in the atomizer. Molecular species can be associated or not to the element of interest. For instance, the molecular bands shown in the figure can be used to determine Ca. Continuum radiation appears as a result of thermal radiation from hot particulate matter in the atomization medium. Molecular bands and continuum radiation are a potential source of interference that must be minimized by proper choice of wavelength, by background correction, or by change in atomization conditions. Molecular flame emission and flame absorption spectra for CaOH Background emission spectra from an ICP. The upper recording was taken favoring continuum and band emission while the lower recording was taken under conditions minimizing continuum and band emission. 105

106 Sample Introduction Methods Achilles heel of Atomic Spectroscopy because in many cases limits the accuracy, the precision and the limits of detection of analytical method. Primary purpose is to transfer a reproducible and representative portion of a sample into one of the atomizers presented in Table 8-1. Table 8-2 lists the common sample introduction methods for Atomic Spectroscopy and the type of samples to which each method is applicable. Atomizers fit into two classes: continuous and discrete atomizers. Continuous atomizers: flames and plasmas. Samples are introduced in a steady manner. Discrete Atomizers: electro-thermal atomizers. Sample introduction is discontinuous and made with a syringe or an auto-sampler. Continuous Discontinuous 106

107 Nebulizers Direct nebulization is the most common method of sample introduction with continuous atomizers. The solution is converted into a spray by the nebulizer. Types of nebulizers: (a) Concentric tube: most common nebulizer. It consists of a concentric-tube in which the liquid sample is drawn through a capillary tube by a highpressure stream of gas flowing around the tip of the tube. (b) Cross-flow: the high pressure gas flows across a capillary tip at right angles. It provides independent control of gas and sample flows. (c) Fritted disk: the sample solution is pumped onto a fritted surface through which a carrier gas flows. It provides a much finer aerosol than a and b. (d) Babington: it consists of a hollow sphere in which a high pressure gas is pumped through a small orifice in the sphere s surface of the sphere. It is less subject to clogging than a-c. It is useful for samples that have a high salt content or for slurries with a significant particulate content. Continuous Atomizer 107

108 Electro-thermal Vaporizers Discrete Atomizer Sample introduction in discrete atomizers is typically made manually with the aid of a syringe. The steps that convert the liquid solution into a vapor of free atoms are the same as those in continuous atomizers. The most common type of discrete atomizer is the electro-thermal atomizer. An electro-thermal atomizer is a small furnace tube heated by passing a current through it from a programmable power supply. The furnace is heated in stages. The dry and ash step removes water and organic or volatile inorganic matter, respectively. The atomization step produces a pulse of atomic vapor that is probed by the radiation beam from the hollow-cathode lamp (HCL). 108

109 Continuous Atomizer Free-Atom Formation in Atomizers Discrete Atomizer Desolvation and Volatilization : desolvation leaves a dry aerosol of molten or solid particles. The solid or molten particle remaining after desolvation is volatilized (vaporized) to obtain free atoms. The efficiency of desolvation and volatilization depends on a number of factors: atomizer temperature, composition of analytical sample (nature and concentration of analyte, solvent and concomitants) and size distribution. In the case of nebulizers, it also depends on the nebulizer design, aerosol trajectories and resident times of the particles. Dissociation and Ionization: in the vapor phase, the analyte can exist as free atoms, molecules or ions. In localized regions of the atomizer, molecules, free atoms and ions co-exist in equilibrium. Dissociation of molecular species: molecular formation reduces the concentration of free atoms and thus degrades the detection limits. The dissociation constant for a molecular species (MX) into its components (MX <=> M + X) can be written as: K d = n M.n X / n MX, where n is the number density (number of species per cm 3 ). For a diatomic molecule: logk d = /2log M M M X /M MX + log Z M Z X /Z MX + 3/2(logT) 5040E d /T where M i is the molecular or atomic weight of species i, Z i is the partition function of species i, E d is the dissociation energy in ev, and T is the temperature in K. Note: The final term in this equation describes most of the temperature dependence: small values of E d and high temperatures lead to large values of K d and thus high degrees of dissociation. Ionization: it can also be consider an equilibrium process: M <=> M + + e -. The ionization constant can be written as: K i = n M+.n e / n M, where n e is the number density of free electrons. The ionization constant can be obtained from: logk i = logz M+ /Z M + 3/2(logT) 5040E ion /T where E ion is the ionization energy in ev. Note: The final term in this equation describes most of the temperature dependence: small values of E ion and high temperatures favor the formation of ions. 109

110 Atomic Absorption (AAS) and Atomic Fluorescence (AFS) Spectrometry The two most common methods of sample atomization encountered in AAS and AFS are flame and electro-thermal atomization. Flame atomization: A solution of the sample is nebulized by a flow of gaseous oxidant, mixed with a gaseous fuel and carried into the flame where atomization occurs. Oxidant (g) Carrier (g) Fuel (g) Note: If the gas flow rate does not exceed the burning velocity, the flame propagates back into the burner, giving flashback. The flame is stable where the flow velocity and the burning velocity are equal. Higher flow rates than the maximum burning velocity cause the flame to blow off. 110

111 Flame Structure Primary combustion zone: Thermal equilibrium is not achieved in this zone and thus it is rarely used for flame spectroscopy. Inter-zonal area: Free atoms are prevalent in this area. It is the most widely used part of the flame for spectroscopy. Secondary combustion zone: products of the inner core are converted to stable molecular oxides that are then dispersed to the surroundings. Maximum temperature: it is located in the flame about 2.5cm above the primary combustion zone. Note: It is important to focus the same part of the flame on the optical beam for all calibrations and analytical measurements. Optimization: of optical beam position within the flame prior to analysis provides the best signal to noise ratio (S/N). It depends on element and it is critical for limits of detection. Increased number of Mg atoms produced by the longer exposure to the heat of the flame. Secondary combustion zone: oxidation of Mg occurs. Oxide particles do not absorb at the observation wavelength. Ag is not easily oxidized so a continuous increase in absorbance is observed. Cr forms very stable oxides that do not absorb at this observation wavelength. 111

112 Commercial Flame Atomizers Typical commercial laminar-flow burner. The aerosol formed by the flow of oxidant is mixed with fuel and passes a series of baffles that remove all but the finest solution droplets. The baffles cause most of the sample to collect in the bottom of the mixing where it drains to waste container. The aerosol, oxidant, and fuel are then burned in a slotted burner to provide a 5- to 10-cm high flame. The quiet flame and relatively long-path length minimizes noise and maximizes absorption. These features result in reproducibility and sensitivity improvements for AAS. AA Spectrometer Excitation source Flame Monochromator Detector 112

113 Cylindrical graphite electrical contacts. These contacts are held in a water-cooled metal housing. Commercial Electro-thermal Atomizers L vov platform. Made of graphite, sample is evaporated and ashed on this platform. Temperature on the platform does not change as fast as it changes in the walls of the furnace. Atomization occurs in an environment where temperature does not change so fast, which improves reproducibility of measurements. Facilitates furnace cleaning, which reduces memory effects. Cylindrical graphite tube where atomization occurs. Dimensions: about 5cm long and 1cm internal diameter. This tube is interchangeable. Output signal Longitudinal (b) and transversal (c) furnace heating. Transversal mode is preferred because it provides a uniform temperature profile along the entire length of the tube and optical path. 113

114 Flame Atomizers versus Electro-thermal Atomizers Advantages of Flame Atomizers Better reproducibility of measurements RSD: Flame 1% Electro-thermal 5% - 10% Much faster analysis times than electrothermal atomizers Wider linear dynamic ranges, up to 2 orders of magnitude wider than electro-thermal atomizers. Advantages of Electro-thermal Atomizers Smaller sample volumes (0.5mL to 10mL of sample) than flame atomizers. Better absolute limits of detection (ALOD to g of analyte) than flame atomizers Note: ALOD = [Sample Volume] x LOD Electro-thermal atomization is the method of choice when flame atomization provides inadequate limits of detection or sample availability is limited. 114

115 Specialized Atomization Techniques Glow-Discharge Atomization Cold-Vapor Atomization Hydride Atomization Hydride Atomization It provides a method for introducing samples containing arsenic (As), antimony (Sb), tin (Sn), bismuth (Bi) and lead (Pb) into the atomizer as a gas. This procedure improves limits of detection 10 to 100x. Their determination at low levels is very important because of their high toxicity. Volatile hydrides are generated by adding an acidified aqueous solution of the sample to a small volume of a 1% aqueous solution of sodium borohydride contained in a glass vessel. A typical reaction is: 3BH 4- (aq) + 3H + (aq) + 4H 3 AsO 4 (aq) 3H 3 BO 3 (aq) + 4AsH 3 (g) + 3H 2 O (l) The volatile hydride is swept into the atomization chamber by an inert gas. The chamber is usually a silica tube heated to several hundred degrees in a furnace or in a flame where atomization takes place. 115

116 Atomic Absorption Instrumentation Main components: (1) Radiation source (2) Sample holder = atomizer (3) Wavelength selector (4) Detector (5) Signal processor and readout Radiation source: Why not using a broadband source with a monochromator for excitation? The emission profile of the source should have a narrower effective bandwidth than the absorption line of the element of interest. HCL and electrodeless discharge lamps (EDL) satisfy this condition. Disadvantage over broadband source/monochromator: One source per element. HCL EDL EDL provide intensities one to two orders of magnitude better than HCL. EDL are only available for fifteen elements. Particularly useful for Se, As, Cd and Sb because it provides better LOD. 116

117 Source Modulation The output of the source is modulated so its intensity fluctuates at a constant frequency. The detector receives two types of signal, an alternating signal from the source and a continuous signal from the flame. A high-pass RC filter is then used to remove the continuous signal and pass the alternating signal for amplification. Source modulation can be done with a chopper or rotating disk or a power supply. Emission from the sample + emission from the flame Monochromator is able to eliminate flame interference based on wavelength separation. However, when the wavelength of interference is the same as the analyte wavelength the monochromator is unable to eliminate interference. High-pass filter H 2 - O 2 Choppers C 2 H 2 O 2 C 2 H 2 -N 2 O 117

118 Spectrophotometers for AAS Single beam and double beam instruments. Double beam instruments provide the advantage of correcting for source fluctuations. In this arrangement, however, the reference beam does not pass through the flame and, therefore, it does not correct for loss of radiant power due to absorption or scattering by the flame itself. Loss of radiant power due to absorption or scattering in the flame could have different sources: (a) fuel and oxidant mixture alone (b) concomitants in sample matrix (c) all of the above When the source of loss of radiant power is only due to the fuel and the oxidant of the flame the solution is simple: make blank measurements and correct analytical data. This type of correction should be done with both types of spectrophotometers, i.e. single and double beam. 118

119 Loss of radiant power due to absorption or scattering from concomitants in the sample matrix Example of spectral matrix interference due to absorption: presence of CaOH in the analysis of Barium. Solution: raise the temperature of the flame. Higher temperatures will decompose CaOH and remove its potential interference. Example of spectral interference due to scattering by products of atomization: most often encountered when particles with diameters greater than the absorption wavelength are formed in the flame: a) Concentrated solutions containing Ti, Zr, and W. These elements form refractory oxides. b) Organic species or when organic solvents are used to dissolve the sample. Incomplete combustion of the organic matter leaves carbonaceous particles. Methods for correcting spectral interference: (1) The two-line correction method (2) The continuum source correction method (3) Zeeman background correction method HCL Scattering l 0 F > l 0 F 119

120 Zeeman Effect It takes place when an atomic vapor is exposed to a strong magnetic field ( 10KG). It consists of a splitting of electronic energy levels, which leads to formation of several absorption lines for each electronic transition. Energy No Yes The simplest splitting pattern is observed with singlet transitions, which leads to a central (p) line and two equally spaced (s) satellite lines ( 0.01nm). A No The central line corresponds to the original wavelength. It has an absorbance that is twice the absorbance of the satellite lines. Both s lines have the same intensity. A p s- s Yes l l 120

121 Background Correction Based on the Zeeman Effect The behavior of p and s lines is different with respect to plane polarized radiation: p lines absorb plane polarized radiation parallel to the external magnetic field (II). s lines absorb plane polarized radiation perpendicular (90 ) to the external magnetic field. 121

122 Ionization Equilibria Ionization of atoms and molecules in atomizers can be represented by the equilibrium: M <=> M + + e - The equilibrium constant for this reaction is: K = [M + ] [e - ] / [M] The ionization of a metal will be strongly influenced by the presence of other ionizable metals in the flame: B <=> B + + e - The ionization of M will be decreased by the mass-action effect of the electrons formed from B. B can then act as an ionization suppressor. Ionization suppressors are often added to the flame to improve sensitivity of analysis. Ionization suppressors are commonly used with higher temperature flames such as N 2 O- acetylene. The concentration of ionization suppressor needs to be controlled to avoid primary inner filter effects, i.e. absorption of excitation radiation. 122

123 Atomic Fluorescence Spectroscopy (AFS) There are five basic types of fluorescence: resonance fluorescence, direct-line fluorescence, stepwise-line fluorescence, sensitized fluorescence and multi-photon fluorescence. The figure shows an energetic diagram level for resonance fluorescence. In all cases, the basic instrumentation is the same. EDL are the best excitation sources for AFS. The advantage of AFS over AAS is that it provides better limits of detection for several elements. Energy 123

124 Atomic Emission Spectrometry The figure shows the typical configuration of a flame or plasma emission spectrometer. There are three primary types of high temperature plasmas: ICP = inductively coupled plasma DCP = direct current plasma MIP = microwave induced plasma ICP and DCP are commercially available. Both types of plasmas sustain temperatures as high as 10,000K. ICP: It consists of three concentric quartz tubes through which streams of argon flows. The diameter of the largest tube is 2.5cm. Surrounding the top of the largest tube is a water-cooled induction coil that is powered by a radio-frequency generator, which radiates 0.5 to 20KW of power at 27.12MHz or 40.68MHz. This coil produces a fluctuating magnetic field (H). Ionization of the flowing argon is initiated by a spark from a Tesla coil. The interaction of the resulting ions, and their associated electrons, with H makes the charges to flow in closed annular paths. The resistance of ions and electrons towards the flow of charges causes ohmic heating of the plasma. The tangential flow of argon cools the internal walls of the ICP. Spectral observations are generally maed at a height of 15 to 20mm above the induction coil, where the temperature is 6,000-6,500K and the region is optically transparent (low background). 124

125 DCP It consists of three electrodes configured in an inverted Y. A graphite anode is located at each arm of the Y and a tungsten cathode at the inverted base. Argon flows from the two anode blocks toward the cathode. The plasma is formed by bringing the cathode into momentary contact with the anodes. Ionization of the argon occurs an a current develops that generates additional ions to sustain the current indefinitely. The temperature at the arc core is between 5,000K and 8,000K. ICP versus DCP: DCP present lower background than ICP. ICP is more sensitive than DCP; LOD in ICP are approximately one order of magnitude better. DCP and ICP have similar reproducibility of measurements. DCP requires less argon usage. ICP is easier to align because the optical window of a DCP is relatively small. Graphite electrodes must be replaced every few hours, whereas the ICP requires little maintenance. 125

126 Instrumentation The main two types of instruments for AES fit into two general categories: sequential or multi-channel spectrometers. Sequential instruments are designed to read one line per element at the time. Multi-channel instruments are designed to measure simultaneously the intensities of emission lines for a large number of elements (50 or 60 elements). Both instruments require wavelength selectors with high spectral resolution. Sequential instrumentation: It uses a slew-scanning monochromator. Hg lamp is used for calibration. Two PMT, one is used for the UV and the other for the VIS. A flipping mirror selects the exit slit and the PMT. 126

127 Scanning Echelle instrumentation It can be used either as a single channel or as a simultaneous multi-channel spectrometer. Scanning is accomplished by moving the PMT in both x and y directions to scan an aperture plate located on the focal plane of the monochromator. The plate contains as many as 300 slits. The time it takes to move the PMT from one slit to another is approximately 1s. This arrangement can be converted to a multi-channel system by placing small PMT behind several exit slits. Polychromators The entrance slit, the exit slits, and the grating surface are located along the circumference of a Rowland circle. The curvature of a Rowland circle corresponds to the focal plane of a monochromator. Each exit slit is factory configured to transmit lines for selected elements. The entrance slit can be moved tangentially to the Rowland circle to provide scanning. 127

128 Charge-Coupled Device Instrumentation Typically incorporates two CCD, one for the UV (165nm 375nm) and one for the VIS (375nm 782nm). The Schmidt cross-disperser separates the UV from the VIS radiation and the orders at each emission wavelength. Elements Determined Tl and Nb curves are not linear probably because of incorrect background subtraction. Self-absorption is another cause of non-linearity. It occurs at high concentrations where the non-excited atoms absorb emitted radiation. 128

129 129

130 An Introduction to Ultraviolet-Visible Molecular Spectrometry (Chapter 13) Beer s Law: A = -log T = -logp 0 / P = e x b x C See Table 13-1 for terms. In measuring absorbance or transmittance, one should compensate for reflections and scatter occurring at the interface of the cuvette. Compensation is always done by running the blank. 130

131 Application of Beer s Law to Mixtures Before applying these equations, you need to know the following: For compound 1: e 1 at l 1 and l 2 For compound 2: e 2 at l 1 and l 2 If their values are not know, you should obtain them via calibration curves. It is also common to obtain e values from single standard solutions. You should always remember: e is a constant that depends on: Wavelength Temperature Solvent e 1 e 2 Absorbance l l 2 Concentration, M

132 Limitations of Beer s Law Three types of limitations cause deviations from linearity: a) Real Limitations b) Instrumental Limitations c) Chemical Limitations Real Limitations: Result from analyte-analyte interactions at high analyte concentrations (usually C > 0.01M). The upper limit of the LDR depends on the compound. For the same compound, it also depends on the solvent and the temperature. You should always determine experimentally the upper limit of the LDR. Absorbance LDR Concentration High analyte concentration causes average distances among analyte molecules to decrease Solute-solute interactions are mainly dipole-dipole interactions Electrostatic interactions can also occur among strong electrolytes 132

133 Chemical deviations: Arise when an analyte dissociates, associates, or reacts with a concomitant (including solvent) to produce a product with different absorption spectrum than the analyte. Typical example: Acid-Base Indicators (HIn). HIn <=> H + + In - (Color 1, l 1 ) (Color 2, l 2 ) Spectrum looks like: => There is a dissociation constant associated to the equilibrium above: Ka = [H + ][In - ] / [HIn] HIn and In - concentrations depend on the ph of solution: [H + ] = Ka x [HIn] / [In - ] => log [H + ] = logka + log [HIn] / [In - ] => - log [H + ] = - logka - log [HIn] / [In - ] => ph = pka + log [In - ] / [HIn] Assuming an indicator with pka = 5 (Ka = 10-5 ): ph log[in - ] / [HIn] [In - ] / [HIn] [In - ] =? X [HIn] At any given wavelength, the total absorbance intensity of the solution is the sum of the individual intensities of HIn and In - : A Total, l A HIn, l + A In-, l 133

134 According to Beer s law, the absorbance intensities of HIn and In - are the following: A HIn, l = e HIn, l. b. [HIn] A In-, l = e In-, l. b. [In - ] Substituting in the total absorbance equation: A Total, l = e HIn, l. b. [HIn] + e In-, l. b. [In - ] => At any given wavelength, the total absorbance intensity of the solution (A Total ) depends on the concentrations of HIn and In -. => Because [HIn] and [In - ] depend on ph, A Total depends on ph. You should also remember that the indicator concentration is given by: C Indicator = C = [HIn] + [In - ] HIn <=> H + + In - C x x x where x = [In - ] = [H + ]. From Ka: Ka = x 2 / C x => x 2 = Ka (C x) => x 2 + Ka.x Ka.C = 0 => x = -Ka ± {Ka 2 + 4KaC} 1/2 / 2 This equation demonstrates that the concentration of indicator varies non-linearly with the ionized fraction of the acid. The same is true for [HIn] ( = C x). A graph of intensity of absorption as a function of concentration of indicator of an un-buffered solution provides a non-linear plot. At 430nm: the absorbance is primarily due to the ionized In - form of the indicator and is proportional to the ionized fraction, which varies non-linearly with the total indicator concentration. At 530nm: the absorbance is due principally to the un-dissociated acid HIn, which increases nonlinearly with the total concentration. 134

135 Instrumental deviations due to polychromatic light Beer s law is only followed when measurements are made with mocnochromatic radiation. Wavelength selection of continuous sources radiation made with filters or monochromators provides a Gaussian wavelength profile with a central wavelength of maximum intensity. Consider a beam of radiation consisting of two wavelengths: Only when the two molar absorptivities are the same, this equation simplifies to A = e.b.c and Beer s law is followed. This condition is best met at the maximum absorption wavelength of the absorber. 135

136 Instrumental deviations in the presence of stray radiation Similar considerations are true for stray radiation. In the presence of stray light radiation (P s ), absorption is given by: A = log [P 0 + P s ] / [P + P s ] Depending on its relative magnitude, stray light radiation can cause significant deviations from linearity. At high stray levels and high concentrations, i.e. strong absorbance and low transmittance, the radiant power transmitted through the sample can become comparable to or lower than stray-light level. Mismatched Cells If the analyte and blank cells are optically different and/or have different path-lengths, deviations from Beer s law can occur. You should always use optically equivalent cells! 136

137 Effects of instrumental noise on spectrophotometric analyses The relative standard deviation (s c /c) of a concentration (c) obtained via a transmittance measurement (T) is given by the equation: s c /c = 0.434s T / T. logt where s T is the absolute standard deviation of the transmittance measurement. This equation shows that the uncertainty in a measurement varies non-linearly with the magnitude of the transmittance. Non-linearity as a function of relative standard deviation is also true for absorbance measurements. The sources of noise (uncertainties) in transmittance (absorbance) measurements can be divided in three cases. K 1, k 2 and k 3 are proportionality constants. Only for Case I s T is independent of T. If the limiting source for uncertainty in a measurement is instrumental noise, the best standard deviation within the calibration curve will then be obtained at the absorbance value where s c /c is minimum. 137

138 Types of Instruments Single channel systems Multi-channel systems Multi-channel systems present the advantage of real-time spectra but the upper concentration limit of their LDR is usually lower than single-beam systems. 138

139 139

140 140

141 Luminescence Spectroscopy Excitation is very rapid (10-15 s). Vibrational relaxation is a non-radiational process. It involves vibrational levels of the same electronic state. The excess of vibrational energy is released by the excited molecule in the form of thermal or vibrational motion to the solvent molecules. It takes between and s. Internal conversion is a non-radiational process. It is the crossover between states of the same multiplicity. It occurs when the high vibrational levels of the lower electronic state overlap with the low vibrational levels of the high electronic state. It can occur between excited states (S 2 and S 1 ) or between excited and ground states (S 1 and S 0 ). Between excited states is rapid (10-12 s). Fluorescence is a radiational transition between S 1 and S 0. It occurs from the ground vibrational level of S 1 to various vibrational levels in S 0. It requires to 10-6 s to occur. External conversion is a nonradiative process in which excited states transfer their excess energy to other species, such as solvent or solute molecules. Intersystem crossing is a non-radiative process between electronic states of different multiplicities. It requires a change in electronic spin and, therefore, it has a much lower probability to occur than spin-allowed transitions. Because the time scale is similar to the one for fluorescence ( s), it competes with fluorescence for the deactivation of the S 1 state Phosphorescence is a radiational deactivation process between electronic states of different multiplicity, i.e. T 1 to S 0. It usually takes between 10-4 to 10s to occur because the process is spin forbidden. 141

142 Intensity of fluorescence (or phosphorescence) emission as a function of fluorophor (or phosphor) concentration The power of fluorescence (or phosphorescence) radiation (F or P) is proportional to the radiant power of the excitation beam that is absorbed by the system: F = K (P 0 P) (1) The transmittance of the sample is given by Beer s law: P/P 0 = 10 -ebc (2) Re-arranging Eq. 1: F = K P 0 (1 P / P 0 ) Substituting Eq. 2 above: F = K (1 10 -ebc ) (3) The exponential term in Eq. 3 can be expanded as a Maclaurin series to: F = K.P 0.[2.303ebc (2.303ebc) 2 + (2.303ebc) 3 - ] (4) 2! 3! For diluted solutions, i.e ebc < 0.05, all of the subsequent terms in the brackets become negligible with respect to the first, so: F = K.P ebc or F = P 0.K.ebc (5) A plot of fluorescence (or phosphorescence) intensity as a function of concentration should be linear up to a certain concentration. Three are the main reasons for lack of linearity at high concentrations: a) 2.303ebc > 0.05 b) self-quenching c) self-absorption Intensity P 0 P F Detector LDR Concentration 142

143 Fluorescence quantum yield The slope of the calibration curve is equal to P 0.K.ebc. K is also known as the fluorescence quantum yield (f F ). The fluorescence quantum yield is the ratio between the number of photons emitted as fluorescence and the number of photons absorbed: f F = # of fluorescence photons # of absorbed photons Fluorescence quantum yields may vary between zero and unity: 0 < f F < 1 The higher the quantum yield, the stronger the fluorescence emission. In terms of rate constants, the fluorescence quantum yield is expressed as follows: f F = kf kf + ki + kec + kic + kpd +kd kf kic kec ki Consider a dilute solution of a fluorescent species A whose concentration is [A] (in mol.l -1 ). A very short pulse of light at time 0 will bring a certain number of molecules A to the S 1 excited state by absorption of photons: A + hν A* The excited molecules then return to S 0, either radiatively or non-radiatively, or undergo intersystem crossing. As in classical kinetics, the rate of disappearance of excited molecules is expressed by the following differential equation: -d[a*] / dt = (kf + knr) [A*] knr = ki + kec + kic + kpd + kd are the rate constants of competing processes that ultimately reduce the intensity of fluorescence. k units = s

144 Fluorescence lifetime Integration of equation: -d[a*] / dt = (kf + knr) [A*] yields the time evolution of the concentration of excited molecules [A*]. Let [A*] 0 be the concentration of excited molecules at time 0 resulting from the pulse light excitation. Integration leads to: [A*] = [A*] 0 exp(-t / t) where t is the lifetime of the excited state S 1. The fluorescence lifetime is then given by: t = 1 / kf + knr Typical fluorescence lifetimes are in the ns range. Typical phosphorescence lifetimes are in the ms to s range. The fluorescence (or phosphorescence lifetime) is the time needed for the concentration of excited molecules to decrease to 1/e of its original value. The fluorescence lifetime correlates to the fluorescence quantum yield as follows: f f = kf. t 144

145 Excitation and emission spectra Excitation spectra appear in the same wavelength region as absorption spectra. However, it is important to keep in mind that absorption spectra are not the same as excitation spectra. Fluorescence and phosphorescence spectra appear at longer wavelength regions than excitation spectra. Phosphorescence spectra appear at longer wavelength regions than fluorescence spectra. In some cases, it is possible to observe vibrational transitions in room-temperature fluorescence spectra. There are several parameters (many wavelengths and two lifetimes) for compound identification. 145

146 Fluorescence and Structure General rule: Most fluorescent compounds are aromatic. An increase in the extent of the p-electron system (i.e. the degree of conjugation) leads to a shift of the absorption and fluorescence spectra to longer wavelengths and an increase in the fluorescence quantum yield. Example: Aromatic hydrocarbon Naphthalene Anthracene Naphthacene Fluorescence ultraviolet blue green Pentacene red The lowest-lying transitions of aromatic hydrocarbons are of the p p* type, which are characterized by high molar absorption coefficients and relatively high quantum fluorescence quantum yields. No fluorescence Fluorescence 146

147 Substituted Aromatic Hydrocarbons The effect of substituents on the fluorescence characteristics of aromatic hydrocarbons varies with the type of substituent. Heavy atoms: the presence of heavy atoms (e.g. Br, I, etc.) results in fluorescence quenching (internal heavy atom effect) because of the increase probability of intersystem crossing (ISC). Electron- donating : -OH, -OR, -NH 2, -NHR, -NR 2 This type of substituent generally induces and increase in the molar absorption coefficient and a shift in both absorption and fluorescence spectra. Electron-withdrawing substituents: carbonyl and nitro-compounds Carbonyl groups: There is no general rule. Their effect depends on the position of the substituent group in the aromatic ring. Nitro groups: No detectable fluorescence. 147

148 Rigidity Rigidity usually enhances fluorescence emission ph of solution Additional resonance forms lead to a more stable first excited state 148

149 Quenching: nonradiative energy transfer from an excited species to other molecules. Quenching results in deactivation of S 1 without the emission of radiation causing a decrease in fluorescence intensity. Types of quenching: dynamic, static and others. Dynamic quenching: or collisional quenching requires contact between the excited species and the quenching agent. Dynamic quenching is a diffusion controlled process. As such, its rate depends on the temperature and viscosity of the sample. High temperatures and low viscosity promote dynamic quenching. For dynamic quenching with a single quencher, the Stern-Volmer expression is valid: F 0 /F = 1 + K q [Q] Where F 0 and F are the fluorescence intensities in the absence and the presence of quencher, respectively. [Q] is the concentration of quencher (mols.l -1 ) and K q is the Stern-Volmer quenching constant. The Stern-Volmer constant is defined as: K q = kq / kf + ki + kic where kq is the rate constant for the quenching process (diffusion controlled). Static Quenching: the quencher and the fluorophor in the ground state form a complex. The complex is no fluorescent (dark complex). The Stern-Volmer equation is still valid but Kq in this case is the equilibrium constant for complex formation: A + Q <=> AQ. In static quenching, the fluorescence lifetime of the fluorophor is not affected. In dynamic quenching, the fluorescence lifetime of the fluorophor is affected. So, lifetime can be used to distinguish between dynamic and static quenching. Quenching Fluorescence quenching of quinine sulfate as a function of chloride concentration Oxygen sensors O 2 is paramagnetic, i.e. its natural electronic configuration is the triplet state. When O 2 interacts with the fluorophor, it promotes conversion and deactivation of excited fluorophor molecules. Upon interaction, O 2 goes into the singlet state (diamagnetic). 149

150 Instrumentation Typical spectrofluorometer (or spectrofluuorimeter) configuration Recording excitation and emission spectra Recording synchronous fluorescence spectra 150

151 Spectrofluorimeter capable to correct for source wavelength dependence Spectrofluorimeter with the ability to record total luminescence 151

152 Measuring phosphorescence Using a spectrofluorimeter with a continuous excitation source: be careful with fluorescence and second order emission! Rotating-can phosphoroscope: good-old approach to discriminate against fluorescence. A. True representation B. Approximate representation t e = exposure time; t d = shutter delay time; t t = shutter transit time; t C = time for one cycle of excitation and observation; t E = t e + t t ; t D = t d + t t Spectrofluorimeters with a pulsed source: employ a gated PMT for fluorescence discrimination. Excitation source on => PMT off = fluorescence decays Excitation source off => PMT on phosphorescence measurement 152

153 Introduction to Chromatographic Separations Analysis of complex samples usually involves previous separation prior to compound determination. Two main separation methods instrumentation are available: based on Chromatography Electrophoresis Chromatography is based on the interaction of chemical species with a mobile phase (MP) and a stationary phase (SP). The MP and the SP are immiscible. The sample is transported by the MP. The interaction of species with the MP and the SP separates chemical species in zones or bands. The relative chemical affinity of chemical species with the MP and the SP dictates the time the species remain in the SP. MP + sample SP Detector Two general types of chromatographic techniques exist: Planar: flat SP, MP moves through capillary action or gravity Column: tube of SP, MP moves through gravity or pressure. 153

154 Classification of Chromatographic Methods Chromatographic methods can be classified on the type of MP and SP and the kinds of equilibrium involved in the transfer of solutes between phases: Column 1: Type of MP Column 2: Type of MP and SP Column 3: SP Column 4: Type of equilibrium Concentration profiles of solute bands A and B at two different times in their migration down the column. 154

155 Migration Rates of Solutes Two-component chromatogram illustrating two methods for improving separation: (a) Original chromatogram with overlapping peaks; (b) improvement brought about an increase in band separation; (c) improvement brought about by a decrease in the widths. Distribution constant or partition ratio or partition coefficient: It describes the partition equilibrium of an analyte between the SP and the MP. If K = K c and SP = S and MP = M K c = c S / C M = n S / V S n M / V M Where V S and V M are the volumes of the two phases and n S and n M are the moles of A in SP and MP, respectively. 155

156 Retention Time Retention time is a measured quantity. From the figure: t M = time it takes a non-retained species (MP) to travel through the column = dead or void time. t R = retention time of analyte. The analyte has been retained because it spends a time t S in the SP. The retention time is then given by: t R = t S + t M The average migration rate (cm/s) of the solute through the column is: Where L is the length of the column. The average linear velocity of the MP molecules is: 156

157 Relationship Between Retention Time and Distribution Constant The Rate of Solute Migration: The Retention Factor Retention factor = capacity factor = k A = k A. However: k A K C or k A K A Where V S and V M are the volumes of SP and MP in the column. Knowing that: => An equation can be derived to obtain K C of A (K A ) as a function of experimental parameters. => 157

158 Band Broadening and Column Efficiency The shape of an analyte zone eluting from a chromatographic column follows a Gaussian profile. Some molecules travel faster than the average. The time it takes them to reach the detector is: t R Dt. Some molecules travel slower than the average molecule. The time it takes them to reach the detector is: t R + Dt The selectivity factor can be measured from the chromatogram. Selectivity factors are always greater than unity, so B should be always the compound with higher affinity by the SP. Selectivity factors are useful parameters to calculate the resolving power of a column. So, the Gaussian provides an average retention time (most frequent time) and a time interval for the total elution of an analyte from the column. The magnitude of Dt depends on the width of the peak. 158

159 Considering that: v_ = L / t R => L = v_ x or L ± DL = v_ x [t R ± Dt] The equation above correlates chromatographic peaks with Gaussian profiles to the length of the column. Both Dt and DL correspond to the standard deviation of a Gaussian peak: Dt DL s If s = Dt, s units are in minutes. If s DL, s units are in cm. The width of a peak is a measure of the efficiency of a column. The narrower the peak, the more efficient is the column. => The efficiencies of chromatographic columns can be compared in terms of number of theoretical plates. 159

160 The Plate Theory The plate theory supposes that the chromatographic column contains a large number of separate layers, called theoretical plates. Separate equilibrations of the sample between the stationary and mobile phase occur in these "plates". The analyte moves down the column by transfer of equilibrated mobile phase from one plate to the next. It is important to remember that theoretical plates do not really exist. They are a figment of the imagination that helps us to understand the processes at work in the column. As previously mentioned, theoretical plates also serve as a figure of merit to measuring column efficiency, either by stating the number of theoretical plates in a column (N) or by stating the plate height (H); i.e. the Height Equivalent to a Theoretical Plate. The number of theoretical plates is given by: N = L / H If the length of the column is L, then the HETP is: H = s 2 / L Note: For columns with the same length (same L): The smaller the H, the narrower the peak. The smaller the H, the larger the number of plates. => column efficiency is favored by small H and large N. It is always possible to using a longer column to improve separation efficiency. 160

161 Experimental Evaluation of H and N Calling s in time units (minutes or seconds) as t: => s / t = cm / s Considering that: v_ = L / t R = cm /s We can write: L / t R = s / t or t s s L / t R v_ If the chromatographic peak is Gaussian, approximately 96% of its area is included within ± 2s. This area corresponds to the area between the two tangents on the two sides of the chromatographic peak. The width of the peak at its base (W) is then equal to: W = 4t in time units or W = 4s in length units. Substituting t = W / 4 in the equation above we obtain: s = LW / 4t R Substituting s = W / 4 in the same equation we obtain: t = Wt R / 4L Substituting s = LW / 4t R in the HEPT equation: H = LW 2 / 16t R 2 Substitution of this equation in N gives: N = 16 (t R / W) 2 These two equations allow one to estimate H and N from experimental parameters. If one considers the peak of the width at the half maximum (W 1/2 ): N = 5.54 (t R / W 1/2 ) 2 In comparing columns, N and H should be obtained with the same compound! 161

162 Kinetic Variables Affecting Column Efficiency The plate theory provides two figures of merit (N and H) for comparing column efficiency but it does not explain band broadening. Table 26-2 provides the variables that affect band broadening in a chromatographic column and, therefore, affect column efficiency. The effect of these variables in column efficiency is best explained by the theory of band broadening. This theory is best represented by the van Deemter equation: H = A + B / u+ C S. u + C M. U where H is in cm and u is the velocity of the mobile phase in cm.s -1. The other terms are explained in Table Table 26-3: f(k) and f (k) are functions of k l and g are constants that depend on the quality of the packing. B is the coefficient of longitudinal diffusion. C S and C M are coefficients of mass transfer in stationary and mobile phase, respectively. Before we try to understand the meaning of the van Deemter equation, a better understanding of chromatographic columns is needed. 162

163 Some Characteristics of Gas Chromatography (GC) Columns Two general types => Open Tubular Columns (OTC) or Capillary Columns => Packed Columns OTC: => Wall Coated Open Tubular (WCOT) Columns => Support Coated Open Tubular (SCOT) Columns => The most common inner diameters for capillary tubes are 0.32 and 0.25mm. Packed Columns: => Glass tubes with 2 to 4mm inner diameter. => Packed with a uniform, finely divided packing material of solid support, coated with a thin layer (005 to 1mm) of liquid stationary phase. Solid Support Material in OTC and Packed Columns Diatomaceous Earth: skeletons of species of single-celled plants that once inhabited ancient lakes and seas. 163

164 Some Characteristics of HPLC Columns Only packed columns are used in HPLC. Current packing consists of porous micro-particles with diameters ranging from 3 to 10mm. The particles are composed of silica, alumina, or an ion-exchange resin. Silica particles are the most common. Thin organic films are chemically or physically bonded to the silica particles. The chemical nature of the thin organic film determines the type of chromatography. SP for normal-phase chromatography Typical microparticle SP for partition chromatography 164

165 Another Look at the van Deemter Equation H = A + B/u + C S u + C M u The multi-path term A or Eddy-Diffusion: => This term accounts for the multitude of pathways by which a molecule (or ion) can find its way through a packed column. A = 2ld p where: l is a geometrical factor that depends on the shape of the particle: 1 l 2. d p is the diameter of the particle. Using packing with spherical particles of small diameters should reduce eddy -diffusion. Injection Detector 165

166 The Longitudinal Diffusion Term B/u: Longitudinal diffusion is the migration of solute from the concentrated center of the band to the more diluted regions on either side of the analyte zone. B/u = 2gD M /u where: g is a constant that depends on the nature of the packing and it varies from 0.6 g 0.8. D M is the diffusion coefficient in the mobile phase. D M a T / m, where T is the temperature and m is the viscosity of the mobile phase. As u infinite, B/u zero. So, the contribution of longitudinal diffusion in the total plate height is only significant at low MP flow rates. Its contribution is potentially more significant in GC than HPLC because of the relatively high column temperatures and low MP viscosity (gas). Initial band Diffusion of the band with time The initial part of the curve is predominantly due to the B/u term. Because the term B/u in GC is larger than HPLC, the overall H in GC is about 10x the overall H in HPLC. 166

167 The Stationary-Phase Mass Transfer Term C S u: C S = mass transfer coefficient in the SP. C S a d f 2 / D S where d f is the thickness of the SP film and D S is the diffusion coefficient in the SP. => Thin-film SP and low viscosity SP (large D S ) provide low mass transfer coefficients in the SP and improve column efficiency. The Mobile-Phase Mass Transfer Term C M u: C M = mass transfer coefficient in the MP. C M a d p 2 / D M where d p is the diameter of packing particles and D M is the diffusion coefficient in the MP. The contribution of mass transfer in the SP and MP on the overall late height depends on the flow velocity of the mobile phase. Both phenomena play a predominant role at high MP flow rates. Liquid SP coated on solid support Cartoon with example of SP mass-transfer in a liquid SP: different degrees of penetration of analyte molecules in the liquid layer of SP lead to band-broadening Porous in silica particle Cartoon with example of MP masstransfer: stagnant pools of MP retained in the porous of silica particles lead to bandbroadening. 167

168 Summary of Methods for Reducing Band Broadening Packed Columns: Most important parameter that affects band broadening is the particle diameter. If the SP is liquid, the thickness of the SP is the most important parameter. Capillary Columns: No packing, so there is no Eddy-diffusion term. Most important parameter that affects band broadening is the diameter of the capillary. Gaseous MP (GC): The rate of longitudinal diffusion can be reduced by lowering the temperature and thus the diffusion coefficient. The effect of temperature is mainly noted at low flow rate velocities where the term B/u is significant. Temperature has little effect on HPLC. Effect of particle diameter in GC Effect of particle diameter in HPLC Note: m = mm 168

169 Optimization of Column Performance Optimization experiments are aimed at either reducing zone broadening or altering relative migration rates of components. The time it takes for chromatographic analysis is also an important parameter that should be optimized without compromising chromatographic resolution. Column Resolution: It is a quantitative measure of the ability of the column to separate two analytes. It can be obtained from the chromatogram with the equation: In terms of retention factors k A and k B for the two solutes, the selectivity factor and the number of theoretical plates of the column: From the last equation we can obtain the number of theoretical plates needed to achieve a given resolution: 169

170 For compounds with similar capacity factors, i.e. k A k B : The time it takes to achieve a separation can be predicted with the formula: Where k = k A + k B / 2 170

171 The General Elution Problem The general elution problem occurs in the separation of mixtures containing compounds with widely different distribution constants. The best solution to the general elution problem is to optimize eluting conditions for each compound during the chromatographic run. In HPLC, this is best accomplished by changing the composition of the mobile phase (Gradient Elution Chromatography). In GC, this is best accomplished by changing the temperature of the column during the chromatographic run. 171

172 Qualitative and Quantitative Analysis in GC and HPLC Both are done with the help of standards. Qualitative analysis, i.e. compound identification is done via retention time. The retention time from the pure standard is compared to the retention time of the analyte in the sample. Note: retention times are experimental parameters and as such are prone to standard deviation. Quantitative analysis is done via the calibration curve method (or external standard method) or the internal standard method. Calibration curve or external standard method: the procedure is the same as usual. The calibration curve can be built plotting the peak height or the peak area versus standard concentration. The same volume of sample was injected in each case, but Sample B has a much smaller peak. Since the t R at the apex of both peaks is 2.85 minutes, this indicates that they are both the same compound, (in this example, acrylamide (ID)). The Area under the peak ( Peak Area Count ) indicates the concentration of the compound. This area value is calculated by the Computer Data Station. Notice the area under the Sample A peak is much larger. In this example, Sample A has 10 times the area of Sample B. Therefore, Sample A has 10 times the concentration, (10 picograms) as much acrylamide as Sample B, (1 picogram). Note, there is another peak, (not identified), that comes out at 1.8 min. in both samples. Since the area counts for both samples are about the same, it has the same concentration in both samples. 172

173 Internal Standards An internal standard is a known amount of a compound that is added to the unknown. The signal from analyte is compared to the signal from the standard to find out how much analyte is present. This method compensates for instrumental response that varies slightly from run to run and deteriorates reproducibility considerably. This is the case of mobile phase flow rate variations in chromatographic analysis. Internal standards are also desirable in cases where the possibility of loosing sample during analysis exists. This is the case of sample separation in the chromatographic column. The internal standard should be chosen according to the analyte. Their chemical behavior with regards to the SP and MP should be similar. How to use an internal standard?: a mixture with the same known amount of standard and analyte is prepared to measure the relative response of the detector for the two species. The factor (F) is obtained from the relative response of the detector. Once the relative response of the detector has been found, the analyte concentration is calculated according to the formula: Area of analyte signal Concentration of analyte = F x Area of standard signal Concentration of standard A known amount of standard is added to the unknown X. The relative response is measured to obtain the detector s response factor F. 173

174 Example of Internal Standards In a preliminary experiment, a solution containing M X and 0.066M S gave peak areas of A X = 423 and A S = 347. Note that areas are measured in arbitrary units by the instrument s computer. To analyze the unknown, 10.0mL of 0.146M S were added to 10.0mL of unknown, and the mixture was diluted to 25.0mL in a volumetric flask. This mixture gave a chromatogram with peak areas A X = 553 and A S = 582. Find the concentration of X in the unknown. First use the standard mixture to find the response factor: A X / [x] = F x {A S / [S]} Standard mixture: 423 / = F {347 / } => F = In the mixture of unknown plus standard, the concentration of S is: [S] = (0.146M)(10.0mL / 25.0mL) = M where: 10.0mL / 25.0mL is the dilution factor Using the known response factor and S concentration of the diluted sample in the equation above: 553 / [X] = (582 / ) =>[X] = M 174

175 Liquid Chromatography Size exclusion or gel: polystyrene-divinylbenzene Silica with various porous sizes 175

176 Instrumentation 176

177 Pumping Systems Pumping systems that allow to change the MP composition during the chromatographic run provide better separation of compounds with wide range of k factors. 177

178 Detectors UV-VIS absorption cell for HPLC 178