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CMH 320 Chapt 5 Lecture 6Chapter 5 Calibration MethodsHomework: Chapt: 5: 5-7, 5-16, 5-17, 5-21, 5-22, 5-23 Due Friday, February 3CMH 320 Chapt 5 Lecture 6Chapter 5 Calibration MethodsCalibration involves developing a functional relationship between signal(s) and concentration(s) of analyte(s)• Signal: response of system (absorbance, current, intensity, ion count, peak area, etc.) This is the dependent or y variable• Concentration: known concentration(s) of analyte(s) in standards. This/these are the independent or x variable(s)CMH 320 Chapt 5 Lecture 6Least squares method is a technique for finding the best line through a given set of points. The technique is based on minimizing the square of the deviations from each point and the line. See Harris pg. 81 – 84 for how to calculate least squares fit.y = 0.2564x + 2.7998R2 = 0.985822.533.544.555.5624681012Δ x = 2.917Δ y = 0.834Least squares method web site:http://standards.nctm.org/document/eexamples/chap7/7.4/#appletSimplest calibration is linear relationship: signal vs. concentrationRecall: Straight line equation - y = mx + bUsing 1stand 2ndpoints:m = Δ y / Δx= 0.834/2.917= 0.213m of line = 0.2564Slight difference, points not perfectly linear.CMH 320 Chapt 5 Lecture 6How do you know if you have a “good” line?(This is not covered in Harris, but is necessary to know!!!)Correlation coefficient: Deviation of the each point from the calculated straight line, listed as an “r” value.Coefficient of Determination: Square of correlation coefficient – this is the value of most importance. Describes the “straightness of the line. Also referred to as the “r2” value.•r2values are from 0 to 1 – the closer the value is to 1, the better the fit of the line.• The r2value can be readily determined with a spreadsheet, and provided when plotting with a treadline (linear regression).CMH 320 Chapt 5 Lecture 6Calibr. Dataage size7.2 4.5811.1 5.5814.0 6.33How tall is a 10 yr old boy?From growth charts at 50%, 10 yr old boy is 4.6 ft tall. This value does not fall on calibration line. WHY???y = 0.257x + 2.7236R2 = 0.999833.544.555.566.56 7 8 9 101112131415age (yr)height (ft)Boy - 50% age 104 ft. 7 in.CMH 320 Chapt 5 Lecture 6To be useful, a calibration curve must:• Have a defined relationship a measurable quantity (usually concentration) and the signal measure.• Often this relationship is linear, but other relationships can also be useful.• Be collected under the same, or near same, conditions as what exists for the analyte.• Similar matrix• Similar species• Similar experimental conditions (sample holder, lab temperature, instrument settings, etc.)• A minimum of 3 data points over a range of concentrations should be collected to define the line (or other calibration relationship). The concentration of the analyte must lie within the calibration range.CMH 320 Chapt 5 Lecture 6An example of acalibration model11001000010000000.001 0.01 0.1 1 10 100I- concentration (ppb)Ions/secCMH 320 Chapt 5 Lecture 6A few things to remember on linear regression• One assumes errors in X are negligible• One assumes that the correct model is picked• Evaluate using standard errors of slope, intercept• Examine “residuals” for funny behavior• Magnitude of r, r2should be examinedCMH 320 Chapt 5 Lecture 6Two reasons why the line is bad: lack of fit, and purely experimental uncertaintyCMH 320 Chapt 5 Lecture 6How to design the calibration set• # settings for X > # parameters in model will allow “lack of fit” to be examined(For example, linear fit: need at least 3 points)• Replicate measurements of Y for a given setting of X will allow “purely experimental uncertainty” to be examinedCMH 320 Chapt 5 Lecture 611.61212.412.80.0033 0.0035 0.00371/Tln k11CMH 320 Chapt 5 Lecture 6Method of standard additions• Known amounts of analyte are added to aliquots of sample• Signals are measured as a function of concentration added• Modeling process: Signal = k*Cadded+ b• Equation is solved for concentration where Signal = 0 (an extrapolation process)CMH 320 Chapt 5 Lecture 6Equations for method of standard additionAnalyte only:Ix= k [Xi] The signal intensity is proportional to theconcentration of the analyte.Analyte + Standard:IS+X= k([Sf] + [X]f) The signal intensity is proportional to theconcentration of the analyte and the standardSO…. Ix/ Is+x = k ([Xi] / k([Sf] + [X]f) = [Xi] / k([Sf] + [X]fTo get Xfand Sf: MUST KNOW DILUTION FACTORS.[Xf] = [Xi] (Vi/ Vf) and [Sf] = [Si] (Vi/ Vf)CMH 320 Chapt 5 Lecture 60123456-0.04 -0.02 0 0.02 0.04 0.06 0.080xyoriginal concentrationExample of Standard Addition PlotCMH 320 Chapt 5 Lecture 6Why is standard addition used?• Std. Add. is effective at correction of “matrix effects”, i.e., the sensitivity (signal/conc) is sample-dependent• Std. Add. will NOT correct for additive interferences, i.e. if another species is present that contributes signal at the sensor being measured.• Std. Add. is standard practice in some techniques.CMH 320 Chapt 5 Lecture 6Internal standardization• A substance known as an “internal standard” is added to samples and standards• Used to correct for drift (changes in sensitivity over time) and matrix effects(sample-related changes in sensitivity)• Effective if certain requirements can be met; less work than std. add.CMH 320 Chapt 5 Lecture 6Requirements for an internal standard• Technique must be multicomponent - must separately measure signals for analyte and internal standard• No interferences: analyte<==> internal std or sample matrix <==> internal std• Internal standard must emulate drift and matrix effect behavior• Internal standard is not native in the sampleInternal Standard Equation (linear)Ianalyte/ Iintstd= k*[Analyte] / [internal std]CMH 320 Chapt 5 Lecture 6What is a blank?• A calibration blank is used to determine the response (signal) given by the measurement system in the absence of any added analyte• Method/preparation/reagent/procedural blank is used to determine the amount of analyte added to the system as a result of the preparation• The blank can either be subtracted from analyte signal, or used as zero point in


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NAU CHM 320 - Calibration Methods

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