Chromatography: basic principles

Transcription

1 Chromatography: basic principles Chromatographic theory is the basis for the development of chromatographic instrumentation and, ultimately, for the application of chromatography to all types of separation problems. In the 1960s the use of gas chromatography (GC) for the separation of volatile organic molecules became widespread. In the 1970s highperformance liquid chromatography (HPLC) took its rightful place in the analytical laboratory for the separation of nonvolatile, thermally labile, ionic, and high-molecular-weight compounds which could not readily be separated by GC. Now HPLC and GC systems are necessary in all types of tasks. All chromatographic separations are based on a common concept: the distribution of components in a mixture between two immiscible phases, one a stationary phase and the other a moving phase. However, for each chromatographic mode the nature of the physicochemical processes can be different. After studying this subject, the students should understand the fundamental theory of chromatography common to all chromatographic modes as well as the basic features that distinguish one mode from another. Based on theory, they can make intelligent dicisions as to the type of chromatography best suited to their particular separation problem. 214

2 The two independent main questions of chromatographic theory are: 1. Which parameters determine the travelling velocity of the sample in the chromatographic system? or Which parameters determine the retention time (or the Rf value)? This question deals with the processes that create separation and it is addressed by the retention theory. 2. Which parameters determine the width of the peaks (of the bands, the spots, etc.)? or Which parameters determine the theoretical plate number (the HETP, the efficiency)? Here we focus on the processes that counteract separation. I. Basic terminology A. Classification of techniques The chromatographic system A chromatographic system consists of two immiscible phases: a mobile fluid phase that streams over a stationary phase. The mobile phase is a liquid, a gas, or a supercritical fluid. The stationary phase may be a porous adsorptive or inert solid, or an ion-exchange resin or a gel. Chromatographic techniques A number of chromatographic names are listed in Table 1 in terms of the combination of phases, mechanisms of retention, and experimental techniques. 215

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4 Experimental methods 1. Elution chromatography (pulse input). This is characterized by the introduction of a small volume of the sample to be analyzed into the flowing mobile phase (eluent) and the observation of the various components of the sample, after their passage through the chromatographic column, in the form of concentration bands or peaks separated in time. This is the major method. 2. Frontal chromatography (step input). This is characterized by feeding the sample continuously into the chromatographic bed (column or layer). The result is observed as a series of concentration steps (frauts), each corresponding to a separate component of the sample. Only the most quickly moving component is (partly) physically separated from the other substances. Used for sampling or cleanup processes. 3. Displacement chromatography. This is a variant of the elution method in which the mobile phase contains components that are more strongly retained by the stationary phase than the sample components under study. This technique is used mainly for preparative purposes. 217

5 B. The concepts of linearity and ideality CENG 5210 Advanced Separation Processes The basis for most chromatographic techniques is a phase equilibrium. A chromatographic system is defined as linear if an isotherm plot is linear and passes through the origin. Linearity is more or less a prerequisite for efficient chromatography and is usually assumed. Therefore, the flow pattern is not altered by the equilibrium. The peaks are symmetrical, with easily defined retention volumes and plate numbers, and the mathematics is manageable. The term ideal implies that there is no peak-broadening mechanism operating. In reality, only nonideal chromatographic systems exist. Nonideal, linear chromatography is the common and preferred case. Ideal, nonlinear chromatography is a hypothetical construction, necessary for obtaining crude descriptions of nonlinear systems. 218

6 II. Characteristics of chromatographic systems A. Fundamental parameters Retention parameters In column elution chromatography, the dominating method, the results of a chromatographic run are obtained in the form of a chromatogram, which is a plot of the response of a detector device and is usually proportional to the flux of material through the detector as a function of time or volume. The retention time (tr) is defined as the time between the instant of sample injection to the column and the peak resulting from a component of the sample. The corresponding volume of gas or liquid is the retention volume (VR). If the flow rate Fc is constant, it holds that VR trfc (1) Usually the maximum of the peak is used to define the retention time, but sometimes the mean or median is used. If the sample component is not retained by the stationary phase but moves entirely within the eluent, its retention time is the mobile phase holdup time tm. The corresponding volume VM is the volume of the mobile phase in the column. By subtraction we obtain the adjusted retention time and volume: t' R tr tm (2) V' R VR VM (3) 219

7 As a normalized measure of retention, we also define a capacity factor k and a retention ratio R as t' V k R ' R (4) tm VM R t M VM 1 (5) tr VR 1 k Hence, tr tm1 k (6) VR VM 1 k (7) In partition chromatography, a distribution coefficient K is defined for the two-phase (gas-liquid or liquid-liquid) equilibrium: K C S (8) CM where CS and CM are the concentrations of solute in the two phases. The basic equation of retention in linear chromatography is VR VM VSK (9) where VS is the volume of the stationary phase. Combining Eqs. (7) & (9) yields VS k V K (10) M In linear chromatography, the velocity ueff of the peak center through the column is a constant if the linear mean flow rate u is constant: u ueff 1 k ur (11) This can be derived from Eq. (6) as t R = L/ u eff and t M = L/u. 220

8 221 CENG 5210 Advanced Separation Processes Dispersion parameters A chromatographic peak is characterized not only by its position (retention time or volume) but also by its width. This is expressed in terms of the variance 2 of the peak, the second statistical central moment. It is convenient to define a dimensionless dispersion parameter, the number of theoretical plates n: 2 t R 2 n (12) with this definition, 2 should be in the unit of time 2. The height of a theoretical plate (HETP) h is defined as L h (13) n where L is the length of the column. Additionally, the number of effective plates N is defined as 2 t' 2 R k N n (14) 2 1 k The term theoretical plate is taken from plate theory, which relates the theory of chromatography to the theory of distillation. To simplify the calculation, the plate number n is sometimes defined as t n R (15) wh where wh is the peak width at half-height. 2

9 The plate height can also be expressed as CENG 5210 Advanced Separation Processes h (16) z where z is the distance of the plate from the column inlet 2 and z should correspondingly be expressed in the unit of length squared. The plate height and plate number depend on many factors, this will be discussed later. 2 z Resolution If two species with different capacity factors are simultaneously introduced into a column, the distance between the centers of the two peaks formed will increase linearly with time: 1 1 z z1 z2 tueff, 1 ueff, 2 tu (17) 1 k1 1 k2 The subscripts 1 and 2 refer to the two peaks, with k1 < k2. At the same time, the width and length for each peak increase only with the square root of t (Eq. 16): z, i zh i tuh i (18) From Eqs. (17) & (18) we see that the resolution, in terms of the distance between the peak divided by the peak width, increases with the square root of time. 222

10 In column elution chromatography, the chromatogram is recoreded as a function of time instead of length. So a standard definition of chromatographic resolution RS is given as tr, 2 tr, 1 RS (19) 21 2 The denominator is the mean of the peak widths, each of which is taken as 4. (For a gaussian peak, about 95% of the peak area is contained between the limits defined by the mean±2.) The term RS may be rewritten in various ways. By noting that tr / n (Eq. (12), & defining k2 / k1, from Eq. (6), we have k n RS 1 1 (20) 2 k1 1 2 By defining a mean capacity factor k k1 k2 / 2, Eq. (20) becomes k n RS 1 (21) 1 1 k 2 If k1 and k2 are very close, which is reasonable since we are usually interested in the resolution of relatively close peaks only, then the resolution may be approximated as k n RS 1 (22) 1 k 4 By using the concept of the effective plate number N, the resolution may be expressed as N RS 1 (23)

11 Eqs. (20) through (23) are different versions of the most widely used separation criterion. The term RS is the product of three factors, each of them emphasizing a different aspect of the separation process: 1. Selectivity, or difference in migration velocities of the two components, reflected as different values of. (RS depends strongly on the value of, especially hen is close to unity) 2. Retention, reflected as different values of k. (The retention factor k / 1 k approaches unity as k is increased) 3. Column efficiency, measured as the plate number n. (RS increases only with the square root of n) Solving Eq. (21) for n, we obtain the required number of theoretical plates nreq necessary to effect a chosen resolution: k nreq R 1 S 1 4 (24) 1 k Similarly, the required number of effective plates is 2 2 Nreq R 1 4 S (25) 1 Often, these terms refer to a separation with RS = 1, which corresponds to a nearly complete separation, in which the distance between the peak centers is equal to 4 (i.e., the peak width at the base). 224

12 Extent of separation The definition of resolution corresponding to Eq. (19) rigorously applies to gaussian peaks only. When peaks are asymmetric, the use of RS may give unexpected and inconsistent results. Additionally, RS is not directly related to the purity of the separated fractions. Since the object of separation is the physical division of one sample into two (or more) fractions, a chromatogram with two peaks should be divided into two regions. The cut point between the regions is usually somewhere between the two peaks. In elution chromatography, the regions separated by the cut point correspond to time periods. If the column effluent is collected in two test tubes, the two regions will be physically separated. The extent of separation is defined as: X11 X21 X22 X12 (26) where Xij is the fraction of component I in region j. The values of range from 0 to 1: if the separation is complete, all of component 1 and none of component 2 is in region 1. Thus, X11 = X22 = 1, and X21 = X12 = 0, so that = 1. With no separation at all, there is an equal amount of both components in both regions, so that all Xij = 0.5, leading to = 0. This concept is very general and may be used to find the optimum cut point between two not necessarily gaussian peaks or to generally optimize chromatographic systems. 225

13 B. Measures of column performance CENG 5210 Advanced Separation Processes Plate numbers A plate number gives only a rough idea of the potential performance of a column, although columns offered for sale by most suppliers are characterized by a single plate number. The limiting plate number If the width of each of a number of peaks produced by a homologous series of chemical compounds is plotted against the capacity factor of each peak, a straight line is often obtained: wh b0 ak (27) The limiting plate number is defined as 2 t n M lim (28) a The theoretical plate number n approaches nlim when k is infinity. The same is true for the effective plate number: lim n lim N nlim (29) k k Hence, nlim is an expression for the column efficiency that is independent of the capacity factor. 226

14 Dispersion and Peak Shapes in Chromatography When a sample zone travels down a chromatographic column, its width is continuously increased owing to various dispersion processes. These include diffusion of solute along the column, resistance to mass transfer between and within phases, and the influence of various flow inequalities and disturbances. The separation resulting from the different velocities of components is counteracted from the dispersion, which decreases the resolution of these compounds. The success of a chromatographic analysis, however, depends not only on the width of peaks but also on their shapes. Peaks that are not narrow and symmetrical, but wide or in various ways deformed ( tailing, leading, and so on), limit the separation and prevent accurate quantification. This also makes sample identification by comparison of retention parameters (time, volume, index) more difficult and arbitary. 227

15 A. Statistical moments A chromatographic peak can be considered a probability density distribution of molecules over time. Then c(t) is the probability that a molecule in the sample is eluted in the time interval (t, t+dt). The normalized sample amount (area of the peak) is m0 0 c( t) dt 1 The definition of the nth zero-point moment mn is n m' n 0 c( t) t dt n 1 The term m1 is the time coordinate of the center of gravity of the the peak, one of the definitions of retention time. The definition of the nth central moment mn is mn 0 c( t) t m' 1 dt n 2 which can also be calculated from zero-point moments by the formula n n! m m i n ' 1 m' n1 i0 i! n 1! 2 The second central moment m2 is the variance t of the distribution c(t), a measure of the width of the peak and, consequently, of dispersion. For a gaussian distribution, m3 = 0. The skew S is defined as m3 S 3/ 2 m 2 n 228

16 The quantity m4 expresses the degree of peak flattening. The excess E is defined as E m 4 3 m m2 For a gaussian distribution, E = 0. A negative value of E signifies a peak that is flatter than a gaussian. Moments can be calculated from experimental peaks with the use of a computer by digitizing the chromatogram with equidistant intervals in the independent variable (time). Moments can also be calculated by curve fitting assuming some special peak shape. 229

17 B. Measures of dispersion CENG 5210 Advanced Separation Processes Theoretical plate number The basic quantity describing dispersion is the variance ( 2 ) of a chromatographic zone, which is the second central moment m2. To express the degree of dispersion, the dimensionless parameter n - the number of theoretical plates - is commonly used, which is defined as 2 m' n 1 m2 n can be calculated by numerical integration. If the peak is gaussian, the following formulas may be used: n t t t t h R R R R w w w A i p 2 h Here, tr is the retention time, wi is the width of the peak at the inflection point (at 60.7% of the height), wh is the width at half-height, wb is the width at the base, hp is the height of the peak, and A is the peak area. Usually the formula with wh is preferred. Plate height The height equivalent to a theoretical plate (HETP), denoted h, is related to n by L h n b 230

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19 Optimizing Separations in Gas Chromatography 1. Triangle of compromise: speed, resolution, capacity and sensitivity Speed Capacity (Sensitivity) Resolution The above figure is the triangle of compromise. It represents the three attributes one strives to optimize in any separation. Each corner is a pure attribute. Inside the triangle corresponds to mixtures of the three attributes. A maximum capacity can be obtained at the expense of minimum speed and low resolution. In reality, a finite column capacity, analysis time, and resolution are always required. So the task of optimizing a given separation centers around the specific needs of the analysis and the capabilities of the available gas chromatography and columns. 232

20 A general approach to optimizing separations in gas chromatography is listed in the following table. Table 1. Approach to optimizing GC analyses 1 Define goals and objectives of the separation. 2 Make initial selection of inlet, detector, column, stationary phase, and carrier gas. 3 Screen sample with fast temperature program and flowrates. 4 Evaluate peak shape, relative concentrations, and elution temperatures. 5 Adjust conditions as necessary to facilitate evaluation and approach analysis goals. 6 Change instrument choices or column if encouraging; repeat steps Repeat screen with widely different temperature program or flowrate. 8 Evaluate sensitivity to temperature/flow, peak shifts, and elution order changes. 9 Fine tune temperature program rate, flowrate to meet goals. 233

21 2. Setting goals This is the most important task in optimizing separations. Common requirements include Specific limit of quantification Analysis time limit Minimum resolution of peaks of interest from each other and interferences Linearity of detector response Finite cost per analysis Compatibility with current chromatographic instrumentation Use of standard columns and consumables Minimum sample consumption Ruggedness Minimum sample degradation Minimum sample handling Goals are usually prioritized by musts and wants; often they have finite limits attached. For example, the analysis must quantify 16 specific organochlorine pesticides at concentrations above 1 ppb, with linear detector response of at least two orders of magnitude, and the results must be confirmed using a second column with different stationary phase. Once goals such as these are defined, the process of narrowing in on an initial instrument configuration and starting conditions can commence. 234

22 3. Overview of variables CENG 5210 Advanced Separation Processes Table 2 summarizes the magnitude and direction of the influence that gas chromatographic variables have on capacity (and sensitivity), resolution, and speed of analysis. It is assumed that only one variable at a time is changed. Proper selection of inlets, detectors, injection parameters, and column format (capillary vs. packed) are critical to meeting analysis goals. The choice of column dimensions and stationary phase can affect aspects of a separation and are difficult to change once chosen, but may be worth taking the time to optimize for high-volume standard methods. Therefore, these require considerable thought before selection is made and optimization is started. Column temperature and carrier-gas flowrate are more easily adjusted and are used to fine-tune separations if scouting runs look promising. 235

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24 4. Selecting the right detector and ensuring appropriate operation Characteristics of common gas chromatographic detectors are summarized in Table 3. Table 3. Detector attributes compared to analysis goals Analysis Goal Universal response Selective response Wide dynamic range Low detection limits Ruggedness Ease of use Molecular information Atomic information Low cost of operation Detectors FID, TCD, MS, IR MS, FPD, NPD, ECD, ELCD, PID, AED FID, MS ECD, SIM-MS, ELCD FID, TCD TCD, FID, (ECD, FPD) MS, IR AED, (ELCD) TCD, FID, ECD For any given detector, manufacturers instructions should be followed to ensure the highest system performance. This includes setting of gas flows and temperature, proper column installation, cleaning, and maintenance. The key is to select a detector that responds only to the components of interest. 237

25 5. Selecting carrier gas and flowrate 5.1 Influence of carrier-gas choice The maximum efficiency and resolution occur when the carrier gas flowrate is at its optimum. This corresponds to the minimum in the van Deemter curve in Figure 2. The optimum flowrate for gases depends on viscosity and diffusion rates. This is a function of the mass of the gas molecule, so optimum flowrates follow the order of H2>He>> N2>>Ar. The shape of the van Deemter curve is much flatter for the lighter gases. 238

26 5.2 Optimum practical gas velocity Doing separations at the optimum flowrate yields the highest efficiencies and theoretically allows one to minimize the length of column required for a separation. However, usually one does not cut columns to shorter lengths, so this advantage is realized only for dedicated analyses. Figure 3 shows that at a given head pressure, linear velocity will decrease as column temperature is increased. This is because gases increase in viscosity with increased temperature - the opposite of liquids. If the head pressure is set to the optimum for a given column and temperature, and the temperature is then increased during the run, the column efficiency will significantly degrade due to the decreases in adsorption affinity and selectivity. 239

27 In capillary chromatography, setting the carrier-gas flowrate to the optimum practical gas velocity (OPGV) ensures maximum efficiency per unit time and prevents loss in efficiency in constant-pressure systems as column temperature is increased. The OPGV (shown in Figure 4) is defined as the point in the van Deemter curve where HETP versus u first becomes linear. The benefit of operating at the OPGV is illustrated in Figure 5. Using longer columns at the OPGV will yield higher resolution in less time than will changing column temperature or flowrate with a given column. 240

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29 6. Selecting the right stationary phase CENG 5210 Advanced Separation Processes 6.1 Packed versus capillary columns Capillary columns are preferred over packed columns for inertness and absolute number of plates (longer columns are possible because of lower pressure drops). A comparison of typical packed and capillary column characteristics is given below. Table 4. Typical packed- and capillary-column characteristics Length Diameter Liquid phase film thickness Phase ratio Capacity Plates/meter Total plates Optimum average linear velocity (He) Void time Plates/sec (k=1.5) Resolution, =1.1 Peak capacity (20 min analysis) Cost Packed 2 m 2 mm 5% wt/wt mg cm/sec 15 sec (k=14) 60 US$100 Capillary 30 m 250 m 0.25 m ng , cm/sec 120 sec (k=2) 275 US$

30 Packed columns are preferred for ruggedness, capacity, compatibility with gas sampling valves, higher selection of polar phases, and low cost. So packed columns are effective for analyses requiring specialized stationary phases, in process (on-line) analysis, and for operators with limited training. 6.2 Selecting stationary phase stationary phases are chosen primarily for their ability to separate the components of interest, but factors such as stability, availability, ease of use, and cost must also be considered. Stationary phases retain solutes through a combination of nonpolar (dispersive) and polar interactions. Dispersive interactions are nonselective. Stationary phases whose major interactions are dispersive (such as methyl silicons) elute compounds based on their molar volumes, or boiling points. Polar stationary phases are often required for analysis of polar compounds. Solutes that are tailed or irreversibly adsorbed on nonpolar columns are eluted with good peak shapes when a polar stationary phase is used. Polarity may also add the selectivity necessary to separate components that coelute on nonpolar phases. 243

31 7. Influence of column dimensions and material Influences of column dimensions on resolution, capacity, and analysis time are summarized in Table 2. To maximize speed of analysis, reduce column diameter or particle size, stationary phase film thickness, and/or column length. To maximize capacity (sensitivity), increase film thickness, column diameter, and/or length of the column. To maximize resolution, increase column length, decrease film thickness, and decrease column diameter. 244

32 8. Screening samples CENG 5210 Advanced Separation Processes 8.1 Evaluation of sample and initial chromatographic choices Once a column, stationary phase, inlet, and detector are chosen and set up, the process of optimizing a separation can begin. The first step is to screen the sample to assess how close the initial choices came to meeting the analysis goals, and to get the approximate elution temperature range of the sample components. This is done using fast analysis conditions - flowrate at OPGV and a temperature program from low to high at o C/min. The low and high temperatures are selected based on knowledge of the sample, solvent boiling points, injection considerations, or from the published temperature limits of the stationary phase being used. If the peak shapes are poor, first correct any reasons for sample or solvent overload and rerun the screen. If the peaks are still unsatisfactory, switch to a different stationary phase of very different polarity. If peak shapes are good but separation of peaks is poor, adjust the temperature program to bracket the elution temperature range for the components and reduce ramp rate by half. Rerun the sample screen. 245

33 8.2 Determine relative sensitivity to temperature Temperature and temperature program rate are the next most useful parameters second to stationary phase type for optimizing separations. The use of temperature program is to shorten the time of analysis. For this, optimization consists only of adjusting the program rate to yield the fastest analysis while meeting goals of resolution and reproducibility. However, it may also take time to cool the oven back down to starting conditions before the next injection. Another advantage of temperature programs is the optimization of separations of closely eluting compounds. This is especially useful when the samples contain compounds with different chemical characteristics. Polar solutes are more sensitive to the temperature change. To evaluate if the separation is sensitive to temperature changes, a new analysis should be done using a different temperature program rate but with the same flowrate, or a different flowrate at the same temperature program rate, because a change in flowrate is associated with temperature effects (the average temperature history changes). 246

34 9. Fine tune temperature program and flowrate 9.1 Fundamental principles of optimization The effect of temperature and flow changes on relative retention is continuous. If an increase in flowrate or temperature program rate improves resolution of a poorly resolved pair of compounds, then further increase will improve separation further within reasonable operating ranges. However, for an extremely fast flowrate or temperature program rate, there will be little retention so no separation. Optimization of temperature and flow involves a few experiments to determine the direction and magnitude of the dependence of resolution on temperature and flow. Visual comparison of chromatograms may be enough to fine tune a separation when a few poorly resolved peaks are involved, but plotting of the relationships and use of graphical approaches often provide better insight, shortens optimization time, and facilitates locating the true optimum. 247

35 9.2 Case study: organochlorine pesticides Table 5 lists 16 organochlorine pesticides that are typically analyzed by GC with ECD. These pesticides have similar structures and are difficult to resolve using nonpolar stationary phase. A 5% phenyl methyl silicon is recommended by EPA as the stationary phase. Table 5. Organochlorine pesticides Peak number Formula C6H6Cl6 C6H6Cl6 C6H6Cl6 C6H6Cl6 C10H2Cl7 C12H6Cl6 C10H4OCl7 C9H6O3Cl6S C12H10OCl6 C14H8Cl4 C12H10OCl6 C9H6O3Cl6S C14H10Cl4 C12H8OCl6 C9H6O4Cl6S C14H9Cl5 Name -Hexachlorocyclohexane -Hexachlorocyclohexane -Hexachlorocyclohexane (Lindane) -Hexachlorocyclohexane Heptachlor Aldrin Heptachlor Epoxide Endosulfan I Dieldrin 4,4 -DDE Endrin Endosulfan II 4,4 -DDD Endrin Aldehyde Endosulfan Sulfate 4,4 -DDT 248

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37 Two pairs of pesticides show the worst resolution, peaks 9/10 and 15/16. As seen in Figure 6, when temperature program rate is changed, the separation of the peak pair 9/10 gets better at higher program rates, whereas the separation of the peak pair 15/16 is better at low program rates. This is plotted in Figure 7. At the intersect, separation of the peak pairs is equal and corresponding to an optimum for this given column and flowrate. However, the optimum temperature program rate is different at different flowrates, with different column lengths, and with different phase ratio. 250

38 Figure 8 shows the dependence of the optimum flowrate versus column head pressure. As head pressure (and therefore flowrate) is increased, the optimum temperature program rate also increases. This is because the optimum separation occurs when the solutes experience the same average temperature before eluting that they did at the lower flow rates. To do this at higher flow rates, the temperature program rate must also increase. This is good if the objective is to minimize analysis time, since both higher flowrates and temperature program rates reduce analysis time. However, the increase in speed is gained at a cost of lower resolution, which is shown in Figure 9. To meet a required resolution of 1.2, the analysis time is 20 min, the temperature program rate is 3.6 o C/min, and the head pressure is 110 psi. 251

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40 Detectors and Data Handling Choosing the right detector for a given separation purpose requires an understanding of the detection mechanisms of each type of detector. Obtaining accurate results with the chosen detector requires an understanding of the dependence of the detector s response on experimental conditions. GC detectors differ from other analytical instruments in that the input to the detector is a flow of separated chemicals. Therefore, it must complete its analysis in a few seconds or less. The sample arrives at the detector completely volatilized and relatively free of matrix effects. Most often the detector is used to quantify known compounds. In the cases of the mass spectrometer (MS), the Fourier transform infrared spectrophotometer (FT-IR), and the atomic emission (AE) detectors, compound identification is their primary purpose. Here we will study the most frequently used detectors and their principles of operation for the correct interpretation of the results obtained. 253

41 1. Parameters of performance CENG 5210 Advanced Separation Processes 1.1 Signal-to-noise ratio Figure 1 shows a portion of a chromatogram illustrating three parameters: the peak height h, the peak width at half its height wh, and the noise N. The peak height is measured in any units from the base of the peak to its maximum. The peak width wb is defined in several ways: (1) the base of the triangle that most closely matches the shape of the peak; (2) twice the width of the peak at half its height; (3) a multiple of the variance, or second moment, of the peak shape; and (4) the ratio (in consistent units) 2A/h, where A is the area of the peak. Method 2 is used here because it is the easiest to measure. 254

42 Noise is the fluctuation of the detector signal when no sample is present. It can be caused by changes in temperature, gas flowrate, line voltage, stability of electronic circuitry, etc. It is a measurement of the average distance between the highest excursion of the baseline and the lowest excursion during a period of time. Most modern electronic integrators measure noise automatically. The baseline can have perturbations other than the noise shown in Figure 1. Figure 2 shows drift and wander. Drift is a slow, constant change of the baseline over time. Drift is often due to temperature change or to column and septum bleed and is often controllable. By contrast, noise is usually due to things within the detector and thus is a more fundamental limit in performance. When the baseline varies randomly over times similar to the peak width, it is called wander, which is distinguished from fast noise. A measurement of noise includes both fast noise and wander, but drift will be ignored. 255 Figure 2. Portion of a chromatogram showing the distinction between drift, fast noise, and wander relative to the peak width at half its height w h.

43 A detector specification often used is the signal-tonoise ratio (S/N). A S/N of 2 indicates a 95% probability that the signal represents a peak if the noise level was evaluated within a time interval corresponding to ten peak widths. The probability is increased to 99% if the signal is 2.65 times greater than the noise. 2. Minimum detectable level The minimum detectable level (MDL) is the quantity or concentration of sample in the detector at the maximum of the peak, when the S/N ratio is 2. This quantity is commonly given as g/sec and is a mass flowrate. The maximum of the peak in Figure 1 corresponds to its height h. If it has a width wb of 20 sec and its area is 570 pg of component, then h would equal 2 times 570 pg divided by 20 sec or 57 pg/sec. If the S/N ratio of the peak is 18, the mass flowrate corresponding to an S/N ratio of 2 would be 57x2/18 = 6.3 pg/sec. This is the MDL. There are some detectors (e.g., thermal conductivity) that respond to the concentration in the detector, rather than the quantity. With these detectors the MDL is dependent on the column flow. In this case 256

44 it is better to let MDL be the concentration of the sample. Often the minimum detectable level is expressed in terms of number of molecules, with units of mol/sec or mol/ml. For detectors that respond selectively to certain elements, the MDL is expressed in g/sec or g/ml, but the weight refers to the weight of the atoms that the detector monitors. Table 1. Minimum detectable level for some detectors Detector MDL Sample compound Thermal conductivity 5x10-10 g/ml Propane (TCD) Flame ionization (FID) Electron (ECD) Flame photometric (FPD) Alkali flame (AFID) capture g(c)/s mol/ml g(s)/s 2x10-12 g(p)/s 5x10-14 g(n)/s 5x10-15 g(p)/s Propane Lindane Thiophene Tributylphosphate Azobenzene Tributylphosphate 3. Sensitivity Sensitivity is defined as the change in detector response with the change in the amount or concentration of the sample. It is the slope of the calibration graph, a plot of detector response vs. analyte concentration or quantity. 257

45 4. Response factor A response factor is a ratio of signal-to-noise size used to characterize a detector. It is independent of carrier flow F and its units reflect the way the detector works, i.e., sensitive to mass or concentration. Table 2. Equation for response factor in terms of weight M of compound injected, peak width wb, and flow F Mass-flow-sensitive detectors Concentration sensitive detectors Based on peak height h hwb/2m hwbfc/2m Area A A/M AFc/M 5. Selectivity When the compounds of interest cannot be resolved from the background, it is practical to use a selective detector for the analysis, which responds to a limited number of compounds. Ideally, the detector would have little or no response to the interesting material and very good response to the compounds of interest. 258

46 6. Linear and dynamic ranges The linear range of a detector is the range of levels of a substance at the detector over which the response of the detector is constant within a specified variation, usually 5%. The lower limit of linearity is the MDL of the substance determined separately. The magnitude of this range is influenced by the choice of test substance. Figure 3 is a plot to demonstrate linearity. A perfectly linear system (including the column) gives a straight, horizontal line. The dynamic range of a detector is greater than the linear range. The dynamic range is defined as the range of levels of a substance over which an incremental change in the level produces an incremental change in detector signal. 259