Pseudo peaks

Fig. 27 Processes involved in the transport characteristics in figure 26. ei = ei,CT, 62 = 62,(7, The red line indicates electron resonant-tunnelling, a) The first conductance peak, b) The second conductance peak, c) The pseudo-peak of conductance, d) The first current maximum, and the red line indicates resonant tunnelling of electrons, e) The second current maximum for electron resonant tunnelling, f) The dip of conductance.

As indicated in Section 5.4.5, it is not appropriate to consider the observed spectral absorption characteristic of a single chromophore as a single function and speak of the half-amplitude points as describing the waveform. The peak wavelength and the two half-amplitude points can be used for less critical work. However, the correct description of the waveform requires that the waveform on each side of the pseudo-peak be plotted as an exponential function and the wavelength specified at which this function is equal to 1/e of its peak value. These two 1/e values properly describe the measured spectral response. 

This effect and similar ones are sometimes responsible for unwanted, unexpected peaks in chromatograms, and then they are called ghost peaks or pseudo peaks. A recent review of this entire subject55 calls them system peaks, and it is a good source of further details and references. 

Broad peaks, ghost peaks, pseudo peaks, negative peaks, peak doubhng, peak fronting, peak tailing, spikes, no peaks. The major causes and their solutions are tabulated in Table 1. 

Samples containing a large excess of iron(Ill) give extremely wide pseudo peaks when the ethylenediammonium tartrate is used. This excess of iron(IIl) will totally obscure the magnesium peak while calcium and strontium appear on the tail of the pseudopeak . 

Simple calculations showed that EDTA does not complex metal ions such as magnesium(II) and calcium(II) at pH 4 but it does complex many other metal cations. Therefore, experiments were performed in which ETDA was added to the metal ion sample and the column was eluted with ethylenediammonium tartrate as before [14]. The amount of EDTA used was more than enough to complex the metal ions present, but an unduly high concentration of EDTA was avoided. The results obtained show that conditions can easily be established whereby magnesium and the alkaline earth cation peaks are hardly affected but metal ions that form stable EDTA complexes at about pH 4 are rapidly eluted. Because EDTA is added only to the sample and not to the eluent, it moves rapidly through the column and appears as part of the pseudo peak . 

Figure 9. A chromatogram of the separation of some common anions monitored by an electrical conductivity detector. Anions l=pseudo-peak, 2=chloride, 3=nitrate, 4=bromide, 5=nitrate, 6=phosphate, 7=(Aiosphite, 8=sulfate, and 9=iodide.

The basic phenomenon was observed in modeling studies by Bjoreskov and Slinko (1965) that sudden increase in inlet temperature caused a transient drop of the peak temperature. The wrong-way response name was given by Mechta et al (1981) after they experienced the opposite a sudden of inlet temperature resulted in an increase of the peak temperature (which may eventually cause a runaway.) The work used a pseudo-homogeneous reaction model and explained the phenomenon by the different speeds of transient response in gas and solid. The example in the last part of Chapter 7.4 explained the speed difference by the large difference in heat capacity of gas and solid phases. For this a two-phase model is needed and spatial and time changes must be followed. 

Likewise, record the second derivative spectra of the four standard pseudo-ephedrine hydrochloride solutions and record the peak heights DL at 258-259 nm plot the results against concentration and confirm that a straight line is obtained. 

Even if the peak behavior fits well for a given apparent desorption order, the real kinetic situation may be a different one. As a rate controlling step in a second-order desorption, random recombination of two particles is assumed most frequently. However, should the desorption proceed via a nonrandom recombination of neighboring particle pairs into an ordered structure, the resulting apparent first-order desorption kinetics is claimed to be possible (36). The term pseudo-first-order kinetics is used in this instance. Vice versa, second-order kinetics of desorption can appear for a nondissociative adsorption, if the existence of a dimer complex is necessary before the actual desorption step can take place (99). A possibility of switching between the apparent second-order and first-order kinetics by changing the surface coverage has also been claimed (60, 99, 100). 

Two-dimensional NMR spectra are normally presented as contour plots (Fig. 3.11a), in which the peaks appear as contours. Although the peaks can be readily visualized by such an overhead view, the relative intensities of the signals and the structures of the multiplets are less readily perceived. Such information can be easily obtained by plotting slices (cross-sections) across rows or columns at different points along the Fi or axes. Stacked plots (Fig. 3.11b) are pleasing esthetically, since they provide a pseudo-3D representation of the spectrum. But except for providing information about noise and artifacts, they offer no advantage over contour plots. Finally, the projection spectra mentioned in the previous section may also be recorded. 

The non-equivalence of the ester protons in the monomethyl- and monophenyl-phosphinic ester function, as in (44, Ch = chalkogen), has been studied. Compounds of type (45) have some interesting stereochemistry. They are prepared from racemic secondary butyl alcohol, and the presence of three signals in the P n.m.r. spectrum confirms that the phosphorus atom is the centre of pseudo-asymmetry. A 1 2 1 triplet is observed which is attributed to the presence of equal amounts of two mesa forms, (45) and (46), which have different values of Sp (outer peaks), and two racemic forms, (47) and (48), which have identical values of 8p (central peak). 

It is often convenient modeling the peak shape assuming some analytical functions [25]. The most commonly used functions are, at present, the Voigt and pseudo-Voigt functions, a combination of a Gaussian (G) and a Lore-ntzian (L) function centered at 20(y. An expression for Gaussian and Lorentzian contributions is ... 

In order to properly take into account the instrumental broadening, the function describing the peak shape must be considered. In the case of Lorentzian shape it is Psize = Pexp - instr while for Gaussian shape p = Pl -Pl tr- In the case of pseudo-Voigt function, Gaussian and Lorentzian contributions must be treated separately [39]. 

So far no hypotheses are required concerning the true shape of the peak profile. Flowever, in order to avoid or reduce the difficulties related to the overlapping of the peaks, the experimental noise, the resolution of the data and the separation peak-background, the approach most frequently used fits by means of a least squared method the diffraction peaks using some suitable functions that allow the analytical Fourier transform, as, for example, Voigt or pseudo-Voigt functions (4) which are the more often used. 

Another typical problem met in this kind of analysis is known as the hook effect . It is due to an overestimation of the background line to the detriment of the peak tails. As a consequence, the low order Fourier coefficients of the profile are underestimated. In the fitting procedure by pseudo-Voigt functions, this problem occurs if the Gauss content is so high that the second derivative of the Fourier coefficients is negative this is obviously physically impossible because it represents a probability density. 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

It is still possible to enhance the resolution also when the point-spread function is unknown. For instance, the resolution is improved by subtracting the second-derivative g x) from the measured signal g x). Thus the signal is restored by ag x) - (7 - a)g Xx) with 0 < a < 1. This llgorithm is called pseudo-deconvolution. Because the second-derivative of any bell-shaped peak is negative between the two inflection points (second-derivative is zero) and positive elsewhere, the subtraction makes the top higher and narrows the wings, which results in a better resolution (see Fig. 40.30). Pseudo-deconvolution methods can correct for sym-... 

---