Sample Analysis Design – Step 2 – Calibration/Standard ...asimonet/ENGV60500/Lecture_8_10_11_2011.pdf · Sample Analysis Design – Step 2 – Calibration/Standard Preparation

Sample Analysis Design Step 2 Calibration/Standard Preparation

Choice of calibration method dependent upon several factors:

1. potential matrix effects

2. number of samples

3. consistency of matrix across samples


EXTERNAL CALIBRATION: Prepare a set of standard solutions to cover the

expected range of analyte concentrations

Fit a least squares regression line

y = mx + b

and calculate analyte concentration in unknowns


23Na calib curve (Medium resolution)

y = 17557xR2 = 0.9992

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44Ca calib curve (Medium resolution)

y = 676.92xR2 = 0.9961

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Advantages of External Calibration

Easy to prepare

Quick

Widely used technique

Sample Analysis Design Step 2 Calibration/Standard Preparation Disadvantages of External Calibration:

Need to matrix match calibration solutions and samples

If standards containing

Sample Analysis Design Step 2 Calibration/Standard Preparation Preparation of External Calibration Solutions:

Need to evenly space calibration concentrations

If the highest concentration is much higher than the rest, linear regression introduces bias favoring the high point

X = independent variable = concentration

Y = dependent variable = counts/second

Sample Analysis Design Standard Addition Method

Aliquots of spike are added to unknown samples to increase the ion signal intensities for elements of interest

Typically use at least three aliquots of sample spiked with evenly spaced amounts of analyte

These spiked aliquots of sample are used to generate a calibration line and calculate the concentration in the sample


S0 = unspiked sample

S1 = sample spiked with analyte at concentration x

S2 = sample spiked with analyte at concentration 2x

S3 = sample spiked with analyte at concentration 3x

S4 = so on and so on


AMT

y = 29387x + 279235R2 = 0.9992

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The concentration of the unknown solution is then determined by dividing the y-intercept value by the slope of the sample-spike mixing line.

From example on previous slide,

Conc. soln = 279235 / 29387 = 9.5 ppb

If the original sample was a solution, then this is the concentration of the analyte in question in the solution


If the original sample was in solid form that you digested and subsequently converted into a solution;

then in order to determine the concentration of the analyte in question, you must factor in the amount of total analyte in the solution and the dry weight of the sample powder


If we continue with the same example, the solution has a concentration of 9.5 ppb, and the original volume of the unknown solution was 10 ml (g) prior to aspirating some of it into the plasma for analysis, then the total amount analyte in the solution is:

= 10 g x 9.5 ng/g (ppb) = 95 ng, or = 0.095 g

If the amount of powder weighed out was 0.1 g, then the concentration of the element in question is:

Conc. = 0.095 g/0.1 g = 0.95 g/g or ppm


This method works best if the slope of the calibration line is not too shallow

This will create more uncertainty in the location of the intersection between the cps of your unknown and the calibration line


For maximum precision its necessary that the amount of sample be the same in each aliquot

Also want the amount of spike added to be the same for each aliquot

Amount of spike added should be as small as possible (usually 0.1 ml to 10 ml total volume)


Ideally, the highest spike concentration should be approximately equal to the concentration of analyte in the unknown

Need to have some idea of the concentration in the sample prior to analysis


Advantages:

Overcomes matrix differences More precise and accurate than external calibration

Disadvantages:

Requires at least three aliquots for each sample Run lengths become much longer and more

preparation time is required

Sample Analysis Design Isotope Dilution

Most accurate and precise calibration method available

Requires analyte with two stable isotopes

Monoisotopic elements cannot be determined via isotope dilution

Spike natural sample with enriched isotope spike of analyte


The amount of spike is selected so that the resulting ratio between spiked isotope and unspiked isotope is near unity maximizes precision

Typically use the most abundant isotope as the reference -- maximizes sensitivity


Check isotope ratio in unspiked sample to determine if the natural ratio in the sample matches with the predicted ratio

If not -- interference in acting on one or both of the isotopes

Always attempt to use interference free isotopes


Prepare the spike to desired concentration

Add spike as early as possible after equilibration of spike and sample you dont have to have complete sample recovery

During any stage of the process complete equilibration is absolutely necessary


Analyze the solution on the ICP using many repetitive scans (to maximize precision)

Need to measure isotopic ratios on standards of a known ratio in order to correct for machine mass discrimination

Use previous equation to calculate concentrations!


Advantages:

Most accurate and precise method for quantitative elemental concentrations

Partial loss of analyte during preparation is compensated for since physical and chemical interferences are not an issue -- will cancel out as they will affect each isotope identically

Ideal form of internal standardization since another isotope of the same element is used in this capacity


Disadvantages:

Generally only applicable to multiple-isotopic elements

Need an enriched isotope spike for the analyte of interest - not always available or sometimes at very high cost

Need two interference free isotopes VERY time consuming

Sample Analysis Design

STEP 3 INTERNAL STANDARDIZATION & INSTRUMENT

DRIFT CORRECTION

Sample Analysis Design Internal Standard

Every sample should be analyzed with an internal standard (IS)

What is an internal standard (IS)?

element that is added to EVERY sample/ blank/calibration standard/QA sample/etc., that is not expected to be in the sample in appreciable quantities and is not an element of interest

use IS to monitor machine drift (both short and long term) and matrix effects


Choice of IS depends upon which elements you are quantifying

The IS should have similar properties in the plasma as element(s) of interest

ICP-MS: similar in mass/ionization potential


Example:

attempting to quantify U - use Th

attempting to quantify most transition metals - use As

attempting to quantify REEs - use Re

115In and 103Rh are common IS for general use

alternatively, you can add several IS to each sample


From previous slide, we assume that samples have little or no Th, As, or Re

Its important to have an idea of whats in your sample prior to quantitative analysis

Solid samples can use a naturally occurring element as IS, provided that you know the concentration in each sample


Procedure for IS use:

Calculate the concentration of the IS in each centrifuge tube the latter will contain an aliquot of your sample and an aliquot of the IS

Divide the measured ion signal (CPS) by the concentration of your IS to derive the factor = CPS/ppb

Divide CPS/ppb of each tube by the CPS/ppb for those measured for the blanks since these are not influenced by possible effects due to sample matrices

The latter yields a dimensionless correction factor (I refer to it as a normalization factor)

Use correction factor to adjust analyte counts for drift or matrix effects


Advantages:

Fluctuations are monitored in each sample/ calibration / blank

Disadvantages:

Assume that behavior of IS is the same as the analyte

Sample Analysis Design Instrumental Drift

Correct for instrument drift with:

Internal standardization is a common procedure

Use of drift corrector solutions (DCS)


Drift Corrector Solutions (DCS):

Measure the same solution intermittently throughout the course of the analytical session

Change in ion signal is assumed to be linear between each DCS measurement


The DCS should contain all elements of interest and can be matrix matched to samples

Example: use standard reference materials (SRMs) for DCS


Apply a linear correction to samples between DCS solutions

DCS1 + ((DCS2 - DCS1)*F)

F = position dependent fraction


Advantages of DCS correction:

all analytes are monitored for drift

nothing added to sample solutions

Disadvantages of DCS correction:

assume change is linear

cannot easily monitor matrix effects

Sample Analysis Design Background & blanks

Standard blank - blank used to monitor polyatomic ion interferences, gas peaks, and contamination from reagents; used for background subtraction

Procedural blank - blank used to monitor contamination acquired during all stages of sample preparation; grinding, digestion, acidification, powdering, etc


Use of blanks during an analytical session:

ALWAYS begin an analytical session with at least one standard blank

Analyze standard blanks periodically throughout the course of the session in particular to monitor memory effects

Process and analyze at least one procedural blank at some point during your research study; for its analysis, its preferable to measure it early in order to avoid any potential memory effects


The more standard blanks that are run during an analytical session, the more information you will have with regards to monitoring change(s) in background levels throughout the entire session


How to determine the background:

1. just use the first standard blank

2. average all standard blanks

3. take median of all standard blanks

4. apply statistical analysis to standard blanks and select some of them


Outlier tests:

1. I know the truth

2. Looks different

3. Statistical proof


Option 1 should be avoided - unscientific and invalid

Option 2 is better but only if the measurement is repeated

Option 3 is the best approach, but needs to be carried out carefully in order to avoid false negatives and positives


Huber Outlier Test

take median of all values

calculate absolute deviation |xi - xm|

take mean of absolute deviations (MAD)

multiply MAD by coefficient (k = 3-5)

anything higher than k*MAD is rejected as outlier


Calculation of Limit of Detection (DL) and Limit of Quantification (QL)

Easy way: LOD = 3*STDEVblank; LOQ = 10*STDEVblank

Sample Analysis Design SUMMARY

A good analytical method will:

1. provide the means to calculate an accurate background level

2. allow for correction of instrument drift

3. use Internal standardization to monitor matrix effects

4. provide some method for monitoring/ correcting interferences

5. Use a proper calibration strategy

Example Calculation Determination of Ca and Na in

beetle blood

Using External Calibration Method

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Sample Analysis Design – Step 2 – Calibration/Standard ...asimonet/ENGV60500/Lecture_8_10_11_2011.pdf · Sample Analysis Design – Step 2 – Calibration/Standard Preparation