Linear mass calibration

Figure 2.243 Linear mass calibration of the quadrupol ion trap analyser (voltage of ring electrode against m/z value).

Doroshenko, V. M. Cotter, R. J. Linear mass calibration in the quadrupole ion-trap mass spectrometer. Rapid Commun. Mass Spectrom. 1994, 8, 766-776. 

Other instrumental advantages include its high sensitivity and a linear mass scale to m/z 10,000 at full sensitivity. The linearity of the mass scale means that it is necessary to calibrate the spectrometer using a single or sometimes two known mass standards. Some calibration is necessary because the start of the mass scale is subject to some instrumental zero offset. The digitized accumulation of spectra provides a better signal-to-noise ratio than can be obtained from one spectrum alone. 

A procedure which enables the response of an instrument to be related to the mass, volume or concentration of an analyte in a sample by first measuring the response from a sample of known composition or from a known amount of the analyte, i.e. standard. Often, a series of standards is used to prepare a calibration curve in which instrument response is plotted as a function of mass, volume or concentration of the analyte over a given range. If the plot is linear, a calibration factor... 

Almost linear OVPD calibration curves of the typical dopant rubrene for a variety of source flows up to 10 seem and up to 50 seem are presented in Fig. 9.9, which shows that the deposition rate can be precisely adjusted from 0.06 to 1.6 A s-1. Both curves are an ideal fit and reveal a linear relationship between deposition rate and source flow they were collected with two mass-flow controllers of different capacity ranges (10 seem and 50 seem). Ellipsometric thickness analysis confirmed for both experiments a deposition rate of 0.3564 and 0.3582 A s-1, which is a relative error of only 0.48% and is identical with our prediction of dopant controllability (Table 9.1). Using a standard OVPD deposition rate of 10 A s-1 for a hosts the doping range of rubrene can be very precisely adjusted in the range of 0-16%. 

Some molecules tend to show multimer formation [M +Adduct]" in ESI, where the adduct can be H, Na, NH4 or otherwise. Some examples are given by Kamel et al. [100-101]. In most cases, only adduct-bound dimers are observed, perhaps of the limited scan range chosen. These multimers can give problems with the unambiguous determination of the molecular mass of an unknown and with the linearity of calibration curve in quantitative analysis. Stefansson et al. [112] reported that the multimer formation of artemisinin, lasalocid, and deoxynivalenol could be reduced by the addition of primary amines. 

Despite these observations, analysing the SEC Rl-elution volume traces with a linear polyethylene calibration curve appears to be valid, in that the short-chain branches did not substantially alter the molecular dimensions. In particular, hydrogenated polybutadienes with 2-5% ethyl branches, an excellent model system for n-butene-1 copolymer systems, elute at the same retention volume as HDPE with the same molecular mass, and they have been used widely as molecular mass standards for HDPE. Unfortunately, the effect... 

Hguro 3 Cause and effect diagram of a titration in which the standard solution is made up from pure solid. (A) Initial diagram with elements from the measurement model (see eqn [1]). (B) Diagram with expanded influence factors. 7=temperature, s =repeatability, cal = manufacturer s calibration (see also eqn [2]). The mass measurements done by difference will contribute only linearity of calibration to the uncertainty labeled cal . 

First, consider the simpler case of a mass-sensitive detector (typically, a differential refractometer, DR) in combination with a molar mass calibration (in turn, obtained from narrow standards of the analyzed polymer). Due to BB (and even in the simpler case of analyzing a linear homopolymer), a whole distribution of hydrodynamic volumes (and therefore of molar masses) is instantaneously present in the DR cell. This establishes that the mass chromatogram w(V) (i.e., the instantaneous mass w vs. the elution time or elution volume V) is a broadened version of a hypothetically true (or corrected) mass chromatogram w (V), as follows ... 

Apart from the use of uniform (or almost uniform) standards, other methods for determining the BB function have been developed. For example, by assuming a uniform and Gaussian BB function with a linear molar mass calibration, it is possible to use the mass and molar mass chromatograms for simultaneously estimating the standard deviation of the BB function and the calibration coefficients.Alternatively, if the shape of the MMD is known (e.g., it is a Poisson distribution on a linear molar mass axis), then the BB function can be estimated from the difference between the (mass or molar mass) chromatogram and its theoretical prediction in the absence of BB. Finally, the BB function can be theoretically predicted from a representative fractionation model. " Unfortunately, however, this approach is so far unfeasible due to the difficulty in determining the associated physicochemical parameters. 

Several (rather restrictive) conditions are here imposed 1) The true mass chromatogram w (V) is Gaussian (for example, because it corresponds to a Wesslau MMD and a linear calibration) 2) the BB function is uniform and Gaussian and 3) the molar mass calibration is linear. Under these conditions, the ad hoc calibrations log M (V), log M (V), and log Mji(V) are all linear and rotated counterclockwise with respect to the unbiased linear calibration log For a non-Gaussian chromatogram, the... 

Fig. 2 Simulated example of DR/LS detection (after Ref. 22). A) Tme and measured mass chromatograms [w (V), w(V)] three samples of the BB function g(V, V) and estimated corrected chromatogram [ (V)]. B) True and measured molar mass chromatograms [. s (V), rLs(V)] and estimated corrected molar mass chromatogram fLs (F)-C) Unbiased linear calibration [log A/(V)1 estimated ad hoc calibration [log M (V)] estimated unbiased calibration [log A/(V)], and estimated linear unbiased calibration [log AfiinXV)]. D) True MMD [w (log A/)] MMD estimate obtained from >v(V) and log M V) [w(log Af)] and MMD estimate obtained from and log Afun.(V)...

Band broadening correction in SEC is still not a totally resolved issue, even when the MMD of a linear homopolymer is determined with a mass detector and a molar mass calibration. Fortunately, modem SEC columns are highly efficient, and the correction for BB is mainly limited to the case of narrowly distributed polymers. Even in the presence of BB, if an instantaneous quality variable is accurately measured, its corresponding global average will also be accurate. 

Like the traditional mass bias correction approaches, the double-spike method also relies on the choice of the mass bias model. The original formalism of the double spikes employed the linear mass bias law and, although double-spike calibration equations adapted for the exponential mass bias discrimination are available, linear models are still often used owing to their simplicity (see, for example, [50-52]). The caveat here is that erroneous results can be obtained when a linear correction is applied to data that do not follow such behavior. This is illustrated below. 

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