Matrix, effects

Matrix effects, which result from the interference of LC co-eluting compounds on the ionization of analytes during the ESI process, induce either ion suppression or enhancement. The effects are matrix-dependent, and ultimately affect the LC-MS quantitative results. Several measures, which include sample extraction, clean-up, dilution, and chromatography, are mandatory and effective to reduce matrix effects. Sample extraction and/or clean-up as discussed in Chapter 4 remove the majority of endogenous compounds present in samples, but a small amount often remains in the final sample extracts. Dilution is the simplest clean-up approach and should be considered first as long as the required detection concentrations are achieved. LC or UHPLC separates analytes from some matrices, which definitely helps to reduce matrix effects. However, no matter what procedures are adopted, matrix effects may not be completely eliminated. Consequently, matrix effects need to be evaluated and compensation is made to achieve the 

To improve the accuracy of LC-MS quantitative results, matrix effects can be compensated for by means of isotopically labeled internal standards, matrix-matched standard calibration curves, standard addition, echo-peak technique, post-column infusion, extrapolative dilution, and so on. Isotopically labeled internal standards and/or matrix-matched standard calibration curves are two common approaches that have been widely used. Table 6.1 lists some commercially available isotopically labeled internal standards. Although this method provides the most accurate result, sometimes it is not realistic to have isotopically labeled standards for each individual analyte. Therefore, matrix-matched standard calibration curves, with or without 

Under certain circumstances, matrix-matched standard curves may not be fit for the intended purpose, for example, when ME is 70% or 110%, due to the complex nature of samples. This approach is also not applicable when there is no blank matrix available. The other techniques mentioned above may provide possible solutions, although these procedures are tedious and require additional sample preparation and calculations. Standard addition is a technique that introduces the standard of a target analyte directly into samples—in other words, a procedure in which 

The echo-peak technique, which simulates the use of an internal standard, is based on two consecutive injections of a reference standard and a sample extract within the same LC analysis. The first and second injections are made to either pass through or bypass a pre-column, respectively. This results in a short difference in retention times between a known amount of reference standard, which is also the analyte of interest, and an analyte from a sample. As a result, the reference elutes close to the analyte. The peak from a reference is referred to as an echo-peak, and the peak from a sample is called a sample peak (Fig. 6.6). Provided that the retention times of these two peaks are close enough, both the reference and the analyte encounter 

Post-column infusion is a technique that utilizes continuous post-column infusion of a representative reference standard, and the response from this standard is used to compensate for matrix effects. This method is based on an assumption that most analytes, even those with diverse physical and chemical properties, will behave similarly in terms of ion suppression or enhancement during the entire chromatographic run in the presence of matrices. Therefore, the response of this representative reference standard at any given retention times of other analytes is possibly utilized to compensate for the matrix effeets for most of analytes. 

Matrix effects influence the correctness of a determined value. They can take the form of constant, systematic errors or of proportional errors 

For example, iron causes proportional errors when determining the nitrite 

Furthermore, it is recommended that k equidistant incremental concentra- 

The incremental volume should be as small as possible in comparison to the sample volume and should be taken in aliquot steps. 

In this way the additional volume VS changes, but the total volume remains constant and is topped up with a solvent (e.g. distilled water) if necessary. 

2 Matrix Effects The matrix effect (the effect of the matrix on the secondary ion yield of a specific element or molecule from which it was emitted) represents one of the primary causes for the difficultly in quantifying secondary ion signals. This is realized as this effect is difficult if not impossible to accurately predict even when analyzing emissions from within a well-defined single matrix. 

Reasons for this stem from the fact that the charge transfer process responsible for secondary ion formation/survival, which ever process it may be (see Section 3.3.1 for possibilities), is highly sensitive to the chemistry of the outermost surface of the substrate at the instant or shortly after the sputtering event. Indeed, the information needed to accurately predict the ionization/neutralization processes active would preclude the necessity of analyzing the respective solid. 

The surface chemistry present at the time of analysis will be a function of the substrate itself (Recall Any element present within the substrate at greater than 1 atomic % will induce its own effect) and any modifications induced before or during the course of analysis. Examples of modifications that can affect secondary ion yields from a Silicon matrix include  

Adsorption of chemically active species before or during analysis. Note Oj can exist even under ultra-high vacuum analysis conditions as discussed in Section 4.2.1.1. 

Implantation of chemically active primary ions such as 0 , O2, Cs, and SFj during analysis. Examples of that resulting from the use of Cs are covered in Section 3.2.2.2.2. 

When a diatomic molecule (guest) is present as a dilute impurity in an inert matrix (host), the selection rules for perturbations and electric dipole allowed transitions can be altered by guest-host interactions. For example, the inevitable absence of cylindrical symmetry (Coot or D h) at a matrix site destroys the distinction between 7r and S orbitals thus A A = 2 transitions [S2 and SO A 3 A— X3E and E-— a1 A (Lee and Pimentel, 1978, 1979) NO 2 — X2II (Chergui, et al., 1988) N2 w1 A — X E+ (Kunsch and Boursey, 1979)] and perturbations (Goodman and Brus, 1977) are quite common. 

The precise nature of a matrix site may be inferred from the occurrence of processes that axe forbidden in the gas phase, the removal of a gas-phase degeneracy (e.g., lifting of e//-orbital degeneracy in A 0 states), or observation of polarization behavior (in amorphous matrices, the degree of fluorescence polarization resulting from linearly polarized excitation or, in single-crystal hosts, the dependence of the absorption cross-section for linearly polarized radiation on the orientation of the crystal axes). 

Removal of the distinction between A = 0 and A 0 states (and the lifting of e/f degeneracy in A 0 states) implies a site with less than threefold rotation 

An unusually good energy match is required before these intersystem relaxation paths compete with more rapid processes such as spin-relaxation within a multiplet state, vibrational relaxation, or spontaneous fluorescence (NO B— X). It is interesting that the B2IIi/2 — a4n5/2 ACl = 2 process seems to require a better energy match than ACl = 1 or 0 processes even though the quantum numbers Cl, A, and E are destroyed by the noncylindrical matrix site. 

Cohen-Tannoudji, C., Diu, B., and Laloe, F. (1977), Quantum Mechanics , John Wiley and Sons, New York. 

The simplest interferences to recognize are those in which a co-eluting compound yields a mass spectrometric signal that coincides or overlaps with that used to monitor the concentration of an analyte such effects 

Suppression of ionization efficiency is important when the total ionizing capability of the ionization technique is limited, so that there is a competition for ionization among compounds that are present in the ion source simultaneously. In principle such a saturation effect must be operative for all ionization techniques, but in practice it is most important for electrospray ionization (Section 5.3.6), slightly less important for atmospheric pressure chemical ionization (Section 5.3.4), atmospheric pressure photoionization (Section 5.3.5) and matrix assisted laser desorption ionization (Section 5.2.2) it does not appear to be problematic under commonly used conditions for electron ionization and chemical ionization (Section 5.2.1) or thermospray (Section 5.3.2). Enhancement of ionization efficiency for an analyte by a co-eluting compound is less commonly observed and is, in general, not well understood. 

The present chapter covers the more fundamental aspects of these ionization techniques, since some appreciation of these principles is essential for an understanding of their respective strengths and limitations, particularly with respect to matrix effects. The most complete discussion of the fundamental aspects is that given in Section 5.3.6a, where the main focus is on electrospray, and their practical implications are described in Sections 9.6 and 10.4.Id. 

To simphfy discussion, it is convenient to categorize the eight ionization techniques of interest here according to whether or not the chromatographic eluant can be introduced directly into the ion source. If not, a discrete device of some sort, distinct from either the chromatograph or the ion source, must be interposed between the 

Standard solutions are the fundamental basis for the accuracy of assays. In preparing standards, it is usually necessary to make a number of assumptions, related to the purity and behavior of the standards. Standards and samples are assumed to react with assay reagents in the same way, and matrix effects are assumed absent. Standard solutions should be dilutions of a stock solution of highly purified material. Often, in the case of a hormone or other complex molecule, the standard is assigned a concentration or unit value based on a comparison with a master standard curve prepared from an international standard. 

As far as is practically possible, the selection and preparation of samples must take into account all possible variations in the matrix of the material to be analysed. The applicability of the method should be studied using various samples ranging from pure standards to mixtures with complex matrices as these may contain substances that interfere to a greater or lesser extent with the quantitative determination of an analyte or the accurate measurement of a parameter. Matrix effects can both reduce and enhance analytical signals and may also act as a barrier to recovery of the analyte from a sample. 

Where matrix interferences exist, the method should ideally be validated using a matched matrix certified reference material. If such a material is not available it may be acceptable to use a sample spiked with a known amount of the standard material. 

The measurement of the recoveries of analyte added to matrices of interest is used to measure the bias of a method (systematic error) although care must be taken when evaluating the results of recovery experiments as it is possible to obtain 100% recovery of the added standard without fully extracting the analyte which may be bound in the sample matrix. 

The whole question of recovery adjustment is a vexed one. In theory, one 

In addition to increasing throughput, researchers are finding ways to utilize the increased sensitivity of the new HPLC-MS/MS systems. For example, Xu et al. [113] recently described the development of a low sample volume assay for preclinical studies. In this assay, only a lO-pL plasma sample volume is required for the analysis. The small volume is prepared by protein precipitation (1 6 = plasmaiacetonitrile) using a special low volume 96-well plate. Only 5 pL of the precipitated sample is injected onto the HPLC-MS/MS system. In spite of these low volumes, the example assay is reported to have a limit of quantitation (LOQ) of 0.1 ng mL h It can be predicted that there will be more reports of improved LOQs and reduced sample volumes as new LC-MS/MS instrumentation is introduced to more laboratories. 

While matrix effects are generally attributed to sample constituents, sample preparation can also lead to matrix effects. Mei et al. [115, 124] demonstrated that matrix effects could be caused by the brand of sample tubes that are used in the sample storage step of the assay. In this example, the solution was to switch to a different supplier for the tubes. In addition, while it is generally reported that 

Inject mobile phase or solvent blank while infusing anaivte into the column eluant at a Row rate of 5 - 10 p.L/miii ami follow path A, 

Inject conti l sample extract while infusing analyte into the column eluant at a flow rate of - 10 pL/min and follow path A. 

Compare the mass chromatograms—differences are due to matrix effects  

The introduction of the sample into the plasma suffers from the same problems in ICP-MS as in ICP emission spectrometry. These include the complicated process of nebulization and atomization. These processes occur before introduction of the sample into the mass spectrometer system. 

The solvent and other elements present in the sample cause matrix effects. These affect atomization efficiency, ionization efficiency, and therefore the strength of the MS signal. This directly impacts quantitative results. Signals may be suppressed or enhanced by matrix effects. Aqueous solutions act very differently from organic solvents, which in turn act differently from each other. 

The problem can be overcome for the most part by matrix matching (i.e the standards used for calibration are matched for acid concentration or solvent, major elements, viscosity, etc., to the matrix of the samples being analyzed). This is similar to AAS and Auger electron spectroscopy (AES) where the same requirement in matching solvent and predominant matrix components is required for accurate quantitative analysis. The use of internal standards will also compensate for some matrix effects and will improve the accuracy and precision of ICP-MS measurements. 

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The sample to be analyzed can be dissolved in an organic solvent, xylene or methylisobutyl ketone. Generally, for reasons of reproducibility and because of matrix effects (the surroundings affect the droplet size and therefore the effectiveness of the nebulization process), it is preferable to mineralize the sample in H2SO4, evaporate it and conduct the test in an aqueous environment. 

For single crystals, matrix effects are largely mled out and excellent quantization has been achieved by... 

The generalized standard addition method (GSAM) extends the analysis of mixtures to situations in which matrix effects prevent the determination of 8x and 8y using external standards.When adding a known concentration of analyte to a solution containing an unknown concentration of analyte, the concentrations usually are not additive (see question 9 in Chapter 5). Conservation of mass, however, is always obeyed. Equation 10.11 can be written in terms of moles, n, by using the relationship... 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

Fluoride-free toothpaste is added as a precaution against any matrix effects that might influence the ion-selective electrode s response. This assumes, of course, that the matrices of the two toothpastes are otherwise similar. 

Ema data can be quantitated to provide elemental concentrations, but several corrections are necessary to account for matrix effects adequately. One weU-known method for matrix correction is the 2af method (7,31). This approach is based on calculated corrections for major matrix-dependent effects which alter the intensity of x-rays observed at a particular energy after being emitted from the corresponding atoms. The 2af method corrects for differences between elements in electron stopping power and backscattering (the correction), self-absorption of x-rays by the matrix (the a correction), and the excitation of x-rays from one element by x-rays emitted from a different element, or in other words, secondary fluorescence (the f correction). 

Sources of Error. pH electrodes are subject to fewer iaterfereaces and other types of error than most potentiometric ionic-activity sensors, ie, ion-selective electrodes (see Electro analytical techniques). However, pH electrodes must be used with an awareness of their particular response characteristics, as weU as the potential sources of error that may affect other components of the measurement system, especially the reference electrode. Several common causes of measurement problems are electrode iaterferences and/or fouling of the pH sensor, sample matrix effects, reference electrode iastabiHty, and improper caHbration of the measurement system (12). 

Spectroscopic methods for the deterrnination of impurities in niobium include the older arc and spark emission procedures (53) along with newer inductively coupled plasma source optical emission methods (54). Some work has been done using inductively coupled mass spectroscopy to determine impurities in niobium (55,56). X-ray fluorescence analysis, a widely used method for niobium analysis, is used for routine work by niobium concentrates producers (57,58). Paying careful attention to matrix effects, precision and accuracy of x-ray fluorescence analyses are at least equal to those of the gravimetric and ion-exchange methods. 

Standards used to constmct a cahbration curve must be prepared such that the matrix of the standard is identical to the sample s matrix because the values of the parameters k and b associated with a linear cahbration curve are matrix dependent. Many areas of chemical analysis are plagued by matrix effects, and it is often difficult to duphcate the sample matrix when preparing external standards. Because it is desirable to eliminate matrix effects, cahbration in the sample matrix itself can be performed. This approach is called the standard addition method (SAM) (14). In this method, the standards are added to the sample matrix and the response of the analyte plus the standard is monitored as a function of the added amount of the standard. The initial response is assumed to be Rq, and the relationship between the response and the concentration of the analyte is... 

Sample pre-treatment. Novel procedures of electrochemical sample treatment have been proposed to decrease the signal interference with native cholinesterase inhibitors present in fruits and vegetables. Polyphenolic compounds were removed by electrolysis with soluble A1 anode followed by the oxidation of thionic pesticides with electrogenerated chlorine. The procedure proposed makes it possible to decrease the background current and the matrix effect by 80-90%. Thus, the detection limits of about 5 ppb of Pai athion-Methyl and Chloropyrifos-Methyl were obtained in spiked grape juice without any additional sepai ation or pre-concentration stages. 

The usage of the ratio of chai acteristic lines as analytical parameter in the process of formation of the calibration curve provides a significant decrease of the residual error. In Realization of this method simultaneously with the decrease of the matrix effects causes some decrease or even full compensation of the fonu and condition of the measured surface. 

THE USE OF INTENSITY OF COHERENT AND NON-COHERENT SCATTERED RADIATION OF THE X-RAY TUBE FOR THE COMPENSATION OF MATRIX EFFECTS AT THE ANALYSIS OF SOLUTIONS BY X-RAY FLUORESCENCE... 

Matrix effects Strong Weak Weak/ medium... 

ICP-OES is a destructive technique that provides only elemental composition. However, ICP-OES is relatively insensitive to sample matrix interference effects. Interference effects in ICP-OES are generally less severe than in GFAA, FAA, or ICPMS. Matrix effects are less severe when using the combination of laser ablation and ICP-OES than when a laser microprobe is used for both ablation and excitation. 

Calibration curves must be made using a series of standards to relate emission intensities to the concentration of each element of interest. Because ICP-OES is relatively insensitive to matrix effects, pure solutions containing the element of interest often are used for calibration. For thin films the amount of sample ablated by spark discharges or laser sources is often a strong function of the sample s composition. Therefore, either standards with a composition similar to the sample s must be used or an internal standard (a known concentration of one element) is needed. 

Nuclear reaction analysis (NRA) is used to determine the concentration and depth distribution of light elements in the near sur ce (the first few lm) of solids. Because this method relies on nuclear reactions, it is insensitive to solid state matrix effects. Hence, it is easily made quantitative without reference to standard samples. NRA is isotope specific, making it ideal for isotopic tracer experiments. This characteristic also makes NRA less vulnerable than some other methods to interference effects that may overwhelm signals from low abundance elements. In addition, measurements are rapid and nondestructive. 

The most accurate - and most popular - method of quantifying matrix effects is to analyze the unknown sample with a similar sample of known composition. The relationship between measured intensity and the content of each sample is, usually, defined by the relative sensitivity factor (RSF) ... 

Under Cs bombardment the matrix effect can be significantly reduced by using the MCs" ion signals for quantification of species M. The detection limit is increased, i.e. the detection power deteriorates, by two or more orders of magnitude, but sometimes even standard-free quantification has been reported [3.51]. MCs" ions have high masses this is a disadvantage because many mass interferences occur in this mass range. 

These theoretical predictions have been verified experimentally for numerous target materials (Fig. 3.53 [3.139]). Note that in Fig. 3.53 there is a pronounced difference between the neutralization of carbon atoms in a carbide and in graphite, respectively. This is one of the rare examples where matrix effects are observed. 

In the discussion so far we have considered the typical LEIS experiment only, i.e. large angles of incidence of exit relative to the surface plane. Under these conditions, in general, quantitative composition analysis is possible, because the ion-target interaction can be considered as a binary collision, because of the absence of matrix effects (see below). 

The usefulness of Eq. (3.41) depends crucially on whether or not the sensitivity factor rjA depends on the presence of other elements in the surface ( matrix effects ). It is an experimental finding that in general neutralization depends only on the atomic number of the scattering center, and matrix effects occur rarely. An instructive example is the neutralization of He by A1 in the pure metal and in alumina. The slopes of the neutralization curves turn out to be the same for both materials, i. e. matrix effects are absent [3.143]. This is a strong indication that in the neutralization process not only the valence/conduction electrons, but also atomic levels below the valence/ conduction band are involved. 

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