Mass calibration equation

While complex, equation (3) provides a suitable mass calibration equation using two or more known product-ion masses. 

Low level data acquisition is the same for peak jump and scan and only differs for continuous and TRA in the handling of the per sweep data. The first step is to convert the acquisition regions, which have been specified in terms of mass, into terms that the acquisition electronics can handle. The mass value of each chaimel in the specified regions is converted to a digital value that the quadrupole electronics can handle by using a mass calibration equation. Once this conversion has been done, the acquisition electronics can acquire a sweep of data. At the end of this sweep the data handling differs depending upon whether this is a continuous acquisition or TRA. 

While it is certainly possible to replace the constant with the appropriate values for constituent parameters ( 2eVID2), it is much more practical to determine the value empirically. A common calibration equation for TOF mass spectrometry is slightly more complicated (with the addition of an offset m/z value, b) and is given by... 

Viscometry is used to measure average molar masses too [1-3]. It is an indirect method, since the measured quantity is the intrinsic viscosity (TV), which is related to the average molar masses calibration by a peculiar formula, called the Mark-Huwink-Sakurada equation [1-3]. 

The evolution of a calibration law for the cubic cell has seen a number of proposals for the frequency-to-mass relationship (26.37-40). Recently, Ledford, et al. (40) developed an algebraically correct mass calibration law (Equation 2), which is now commonly used. Unlike sector mass spectrometry in which many... 

The major application of high resolution mass spectrometry is for obtaining accurate mass measurements in order to determine elemental compositions. The present FTMS calibration equation, derived by Ledford, et al. [14] shows that the mass-to-charge ratio m/z of a given ion is related to the magnetic field, B, the electric field, E, and the measured frequency, F, by a relation having the form ... 

It is also possible to improve the accuracy of the mass calibration by making use of a peak of known composition to correct the electric field term for changes in the number of ions [16], In other words, if the identity of some component of the mixture is known by its retention time and/or mass spectrum, a peak of known mass in the mass spectrum may be used to apply a correction factor, x, to the electric field term in the calibration equation, which may be rewritten as ... 

The process model can be obtained by different forms, and in bioprocesses mass balance equations canprovide much information. However, in order to have efficient process models and software sensors, a previous adjustment of the model is necessary using on-line data collected from a plant under different operational conditions. This databank is important to guarantee that the model remains calibrated and represents the plant adequately. Some requisites are indispensable for the experimental implementation of models in software sensors response speed to disturbances in the system and appropriate inference of primary variables of interest during key points of the process. 

Calibrate the spectra to ensure reliable mass accuracy. Generate a calibration equation using calibrants that cover the mass range of interest, and then match the calibrant and sample matrix. External mass calibration can subsequently be applied to the relevant spectra. 

Another interesting characteristic of the TOF analyser lies in its easy mass calibration with only two reference points. As in all the mass spectrometers, the TOF mass spectrometer requires a calibration equation to relate and convert the physical property that is measured to a mass value. For the TOF spectrometer, the physical property that is measured during an analysis is the flight time of the ions. As already mentioned, the flight time of an ion is related to its mass by the following equation ... 

Diblock copolymers of PS-PDMS were chosen for study because PS and PDMS homopolymers in good solvents have the same molar mass calibrations in SEC (23). For PS and PDMS homopolymers in tetra-chloroethylene, it can be shown from data for intrinsic viscosity that the Mark-Houwink exponent for both of these polymers is near 0.8 (9). Equations for universal calibration (24) indicate that an M(PS-PDMS) diblock copolymer calibration should therefore follow that for the corresponding homopolymers. Consequently, there should be a narrow range of masses at each elution volume, so that the term containing Pi in equation 7 can be ignored and can be replaced by Mi, giving... 

Y is the expected response and X is the corresponding concentration. A, B,C and D are the four parameters of the equation, where A gives an estimate of expected response at zero dose, B is the slope (e.g., response/concentration) in the middle of the calibration curve, C is the IC50 and D is the expected response at infinite dose. This curve satisfies all the conditions specified for the response-concentration relationship and also closely approximates the mass-action equations [20]. Weighting of the results is recommended for fitting dose-response data from immunoassay, in order to compensate the heterogeneity of response variances in the response-error relationship [17,18]. 

The mathematical treatment of FMC data can be accomplished by standard procedures via the solution of mass balance equations, on condition that the data were converted to reaction rate data with Eq. (21). As mentioned above, this requires the determination of the transformation parameter a. Two approaches based on calibration were developed and tested. In the first approach, thermometric signals are combined with the absolute activity of IMB, which had been determined by a separate measurement using an independent analytical technique. Figure 5 shows a calibration for the cephalosporin C transformation catalyzed by D-amino acid oxidase. The activity of the IMB was determined by the reaction rate measurement in a stirred-tank batch reactor. The reaction rate was determined as the initial rate of consumption of cephalosporin C monitored by HPLC analysis. The thermometric response was measured for each IMB packed in the FMC column, and plotted against the corresponding reaction rate. From the calibration results shown in Fig. 5 it can be concluded, independently of the type of immobilized biocatalyst, that the data fall to the same line and that there is a linear correlation between the heat response and the activity of the catalyst packed in the column. The transformation parameter a was determined from... 

Heavy-ion spectroscopy is different from that of lighter charged particles because of the pulse-height defect (PHD), which makes the energy calibration equation mass dependent. 

Since it is only valid to compare like averages with each other in a calibration of this kind, the question arises as to what kind of molar mass average is obtained from Equation (9-151). According to Equation (9-125), the intrinsic viscosity of a polymolecular substance is a mass average. Equation (9-151) can thus be written as... 

When one injects a branched polymer into the SEC column, it will elute at early times (with respect to its unbranched analog that possesses the same molar mass). This is due to the fact that branched polymers are very compact In particular, the slope hi, which appears in the calibration equation (Eq. 2.25), is large. Also cyclic oligomers elute earlier than do linear oligomers of the identical type. 

The measured arrival times of all ions provides a time spectrum that is converted into a mass spectrum by calibrating the instrument. A generally accepted calibration equation is... 

Dudley [54] has described in detail the characterization of nylon-66 by SEC. Nylon samples were initially fractionated from a mixed solvent of phenol and water, and the number average molecular weight of the fractions measured by membrane osmometry in m-cresol at 105°C. The intrinsic viscosities of the fractions were also measured, as well as their SEC in m-cresol at 130°C. The chromatograms were analysed using a molecular mass calibration based on polystyrene standards and using a g-factor for nylon-6 6 of 13.9. The Mark-Houwink equation was then determined as... 

The frequencies observed are converted to mass values using a calibration equation. There are several different equations that are functionally equivalent [69-71] (these have recently been reviewed [72]), but the most accepted equation is... 

Calibration of peak position for accurate mass determination can be performed internally or externally to minimize systematic errors. Internal calibration can be conducted when compounds with known molecular weight (called calibration compounds or calibrants) are mixed with the sample prior to the introduction into the ion source. This calibration can be performed, for example, by adding the calibrant to the liquid-phase sample while diluting it prior to analysis. The best result is achieved when multiple calibration signals are used to interpolate the m/z of ions within the range of interest. In proteomics, a tryptic digest of albumin from horse heart is typically used as the calibrant because it covers a wide m/z range (e.g., m/z 800-3000) that is ideal for mass calibration of low- to medium-sized peptides. In external calibration, the calibrants are analyzed before the analysis of real samples. The peaks of the calibrants are used to create and set the calibration equation in the data acquisition software. This method provides less mass accuracy because the instrument condition may still vary between the calibration and analyses of real samples. However, external calibrations save time and calibration compounds, and such methods also make analyses of analytes free from interferences caused by calibrants. 

ANNs represent one of the most powerful model free methods. It has been shown recently that the stability constants can be calculated even without solving mass balance equations applying a multivariate calibration approach and the ANN method. The procedure is in some way analogous to Sillen s so-called projection maps, described in the 1960s [82,83]. The projection maps method has even been computerized, but the evaluation is done graphically [84]. 

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