Peak Separation width

Consider the separation depicted in Figure 1. It is assumed that the pair of solutes represent the elution of the solute of interest and its nearest neighbor. Now, when the sample volume becomes extreme, the dispersion that results from column overload, to the first approximation, becomes equivalent to the sample volume itself as the sample volume now contributes to the elution of the solutes. Thus, from Figure 1, the peak separation in milliliters of mobile phase will be equivalent to the volume of sample plus half the sum of the base widths of the respective peaks. 

The peak-shaped response of differential-pulse measurements results in unproved resolution between two species with similar redox potentials, hi various situations, peaks separated by 50 mV may be measured. Such quantitation depends not only upon the corresponding peak potentials but also on the widths of the peak. The width of the peak (at half-height) is related to the electron stoichiometry ... 

To determine the band dispersion that results from a significant, but moderate, sample volume overload the summation of variances can be used. However, when the sample volume becomes excessive, the band dispersion that results becomes equivalent to the sample volume itself. In figure 10, two solutes are depicted that are eluted from a column under conditions of no overload. If the dispersion from the excessive sample volume just allows the peaks to touch at the base, the peak separation in milliliters of mobile phase passed through the column will be equivalent to the sample volume (Vi) plus half the base width of both peaks. It is assumed in figure 10 that the efficiency of each peak is the same and in most cases this will be true. If there is some significant difference, an average value of the efficiencies of the two peaks can be taken. 

Peedc-to-peak resolution in SEC can be calculated by the ratio of peak separation at the peak maxiaut to the sum of the baseline peak widths. This general definition of resolution is less useful in SEC, where a measure of the ability of the column to separate solutes of different molecular weight is required. For this purposes, we define a new term, the specific resolution factor, R, which relates peak resolution to sample molecular weight, assuming all measurements are made within the linear region of the molecular weight calibration curve, equation (4.41)... 

At either frequency the sensitivity of the instrument is quite remarkable. The exact signal-to-noise ratio depends upon a number of factors including apparent line width (including g and hyperfine anisotropy), ease of saturation, the temperature, and the linear density of the sample in the quartz tube. For a relatively narrow line with peak-to-peak separation of two gauss it is possible to observe the spectrum for concentrations as low as 1014 spins per gram of sample. As the spectrum becomes more anisotropic, the sensitivity of course decreases. Lowering the temperature increases the sensitivity since the population difference An increases [(Eqs. (26) and (3°)]. 

Resolution, R is measured from a chromatogram by relating the peak-to-peak separation to the average peak width. This is expressed by the equation... 

Fig. 4 Restoration of Cygnus A astronomical radio source at 11 cm by Biraud s method. Dash-dotted curve, recorded measurement solid curve, deconvolution, a = 0.89, b = beam width at half power. The ordinate is intensity given in arbitrary units. The peak separation is 104 arcsec (Biraud, 1969).

When two Gaussian peaks (i and j) are close, resolution (Rs) is defined as the peak separation divided by the mean peak width ... 

If only adsorbed forms of ox and red are electroactive, then the voltammetric peaks are sharp and symmetrical (the current rises from zero to a maximum value and then falls again to zero, and there is little or no peak separation).39 41 The symmetrical, sharp peak results from the fixed amount of the reactant that is adsorbed on the electrode. The values of ip, Ep, and the peak width depend on the type of adsorption isotherm involved and relative strength of the adsorption of oxidized and reduced species on the electrode surface. If the adsorption is described by a Langmuir isotherm, Epc = p a and the peak current is described by... 

As was discussed in Chapter 1 resolution, R, is a measure of the distance between two adjacent peaks in terms of the number of average peak widths than can fit between the band (zone) centers. Assuming symmetrical (Gaussian) peaks, when R = 1, peak separation is nearly complete with only about 2% overlap. This case was shown in Chapter 1, Figure 1-4. Resolution results from the physical and chemical interactions that occur as the sample travels through the column. It should, therefore, be no surprise that resolution may also be expressed in terms of the contribution of the individual column characteristics separation factor (selectivity, a), efficiency (narrowness of peak, N), and capacity factor (residence time, k ) of the first component. The equation that describes this interrelationship is... 

The absorption and emission bands have gaussian line shapes with their peaks separated by 2fV, as is illustrated in Fig. 8.4. The difference in energy is known as the Stokes shift as the strength of the electron-phonon coupling increases, so do the Stokes shift and the line widths. 

In addition to evaluation of line widths and peak separations, analysis of T values and spin saturation transfer can be performed to access a wide range of timescales. Under conditions of slow exchange between forms A and B and upon irradiation at vb, the time constant associated with state A (ta) can be determined from the measured T of nucleus A in the presence of exchange and the T of nucleus A in the absence of exchange ... 

The first theoretical studies on AI2O3 were of electronic structure and spectra. Photoelectron studies on AI2O3 (Balzarotti and Bianconi, 1976 Gignac et a ., 1985) show a two-peak O 2p valence band with a peak separation of 4-4.7 eV and an overall width of about 8.5 eV (Fig. 4.7). Cluster calculations using the MS-SCF-Aa method (Tossell, 1975a), and the semi-empirical molecular-orbital EHMO (Ciraci and Batra, 1983) and CNDO... 

Material for analysis can be recovered or examined by determination of either the distribution of a solute in a series of tubes or its distribution as it is eluted from such a series. To indicate quantitatively the effectiveness of the selective separation of one substance from another, the term resolution may be used. Resolution of bands may be defined as the ratio of band separation to average band width, and similarly, resolution of peaks as the ratio of peak separation to average peak width (Section 24-6). 

Two solutes will be resolved if their peaks are moved apart in the column and maintained sufficiently narrow to permit them to be eluted as discrete peaks. Resolution is usually defined as the ratio of the distance between the peaks to the peak width at the points of inflection. It is generally accepted that a separation of 4a is adequate for accurate quantitative analysis, particularly when employing peak heights measurements. It is, therefore, necessary to derive an expression for the peak width in order to equate to the peak separation. 

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