Resolution Rs

Defining separation in terms of the selectivity factor (equations (2.41)-(2.43)) ignores the effects of peak width and band broadening. The resolution factor (Rs) is defined by equation (2.44), which takes into account both the difference in retention as well as the average peak widths of the two peaks (0.5(wb,i + Wa,i)) (Knox, 1977). 

1 Factors influencing resolution. If the difference in retention times of the two peaks is small ( 6a), then the resolution factor may be approximated by 

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Resolution. The degree of separation or resolution, Rs, of two adjacent peaks is defined as the distance between band peaks (or centers) divided by the average bandwidth using 14), as shown in Fig. 11.3. 

It is difficult to compare separation techniques in any general way. Comparison may be based on the traditional figures of merit, such as resolution Rs (including column efficiency N, selectivity, retention, and peak capacity), chromatographic speed, sample capacity, sensitivity, detection and column impedance, as well as breadth of application. Usually a tradeoff between these attributes is found. Berger [26] has compared GC, pSFC, cSFC, LC and CE on the basis... 

According to Equation 3, the resolution Rs of two peaks in column separation is controlled by three major variables retention defined in terms of the retention factor k column efficiency expressed as the number of theoretical plates N and selectivity characterized by the selectivity factor a [48] ... 

What we are looking for in a chromatographic separation is to achieve satisfactory resolution of our solutes in the minimum amount of time. Resolution (Rs) describes the degree of separation of one component from another, and is defined as the difference in retention volumes of the two solutes divided by their average peak width. 

Resolution The chromatographic separation of two components, A and B, under trace conditions with small feed injections can be characterized in terms of the resolution, Rs. For nearly Gaussian peaks ... 

From the data presented above, use adjacent peak pairs to calculate selectivity (a) and resolution (Rs). 

A common but very important goal in HPLC is to obtain adequate separation of a given sample mixture. To achieve this goal, we need to have some quantitative measure of the relative separation or resolution achieved. The resolution, Rs, of two adjacent peaks 1 and 2 is defined as equal to the distance between the center of two peaks, divided by average peak width (see Fig. 15.3) ... 

In general, the resolution (Rs) between two peaks in chromatographic and related separation techniques is determined by the efficiency of the column and the selectivity of the separation [10] ... 

The efficacy of the separation of two neighbouring spots is defined by the resolution Rs. It can be calculated by... 

In order to evaluate the efficacy of the expanded bed technique the plate height (HETP), plate number (N), resolution (Rs), Bodenstein number (Bo), particle Peclet number (Pep) and axial dispersion coefficient (DJ have been calculated and compared with the corresponding values of a traditional HPLC column. N can be expressed by... 

The resolution between two solute components achieved by a column depends on the opposed effects of (a) the increasing separation of band centres and (b) the increasing band width as bands migrate along the column. The resolution Rs is defined by ... 

The resolution, Rs, is used to describe the separation conditions of two compounds. The Rs value is given by the ratio of the distance between... 

Thus when ri,f and L are constant, shortening the analysis time can be achieved by increasing the pressure drop and the k° value. Increasing k° can be done by decreasing s and/or increasing the particle size, dp, of the stationary phase material. Increasing the particle size decreases the resolution, Rs therefore, small particle-size stationary phase materials must be densely packed. As a result, a high-pressure operation is unavoidable. 

Resolution (Rs)> 1, 96, 101 Retention volume (CR), 4 Reversed-phase ion-pair, 8 Reversed-phase, 7, 8, 57... 

As a general rule, in the case of CSPs featuring hydrophobic pockets, a decrease of mobile phase flow-rate results in an increase of chromatographic resolution (Rs), as a consequence of better stationary phase mass transfer [78]. This change has significant impact mostly in RP mode [17]. In the NP enantioselective separations of two test solutes (4-hexyl-5-cyano-6-methoxy-3,4-dihydro-2-pyridone and... 

FIGURE 4.1 Effect of the plate number (N), the separation factor (a ), and the retention factor (k) on resolution (Rs). (Adapted from Sandra, P.J. 1989. High Resolut. Chromatogr. 12 82-86. With permission.)... 

FIGURE 4.3 Separation of metoprolol enantiomers by LC and SFC on a Chiralcel OD stationary phase. Conditions (a) The LC separation was performed with 20% 2-propanol in hexane with 0.1% (v/v) diethylamine at 0.5 mL/min, selectivity (a) = 2.67, and resolution (Rs) = 4.8. (b) The SFC separation was performed with 20% methanol, which contained 0.5% isopropylamine, in carbon dioxide at 2.0 mL/min, 15MPa, and30°C a = 2.77,andRs = 12.7. (Adapted from Phinney, K.V. 2000. Anal. Chem. 72 204A-211A. With permission.)... 

In chromatographic and related separation techniques the basic requirements for the resolution (Rs) of two peaks are a column with a high number of plate counts and a factor to induce some selectivity for the separation. Basically resolution is the product of separation efficiency and selectivity ... 

In the System Suitability section, different parameters are described which can be applied in order to check the behavior of the CE system. The choice of the appropriate parameters depends on the mode of CE used. The system suitability parameters include retention factor (k) (only for MEKC), apparent number of theoretical plates (N), symmetry factor (Af), resolution (Rs)> Rtea repeatability, migration time repeatability, and signal-to-noise ratio. Practical equations to calculate different system suitability parameters from the electropherograms are presented, which are also included in Table 3. 

Relative standard deviations for the mean resolution (Rs) were... 

Figure B4.2.2 Hypothetical chromatogram illustrating calculation of elution volumes and peak widths for two peaks. Total elution volume is plotted against absorbance at 280 nm. Vri and Vr2 are the elution volumes (at the peak maxima) of peaks 1 and 2, respectively Wb1 and Wh2 are the peak widths (at base) of peaks 1 and 2, respectively. Peak widths at base represent the segment of the baseline intercepted by the tangents drawn to the inflection points of the peak. Resolution (Rs) is defined as the distance between the elution volumes at peak maxima divided by the average of the peak widths, according to Equation B4.2.1 (see Resolution).

Figure G1.4.4 Resolution Rs = 2AfR/(lVbi + Wb2) at different separations. (A) sufficient separation, Rs = 1 (B) baseline separation, Rs = 1.5. C, D, and E have the same separation factor, but show problems cause by overloading the column. (C) Good resolution (D) some peak broadening and tailing (E) excessive tailing causing peak overlap.

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

The resolution, Rs, of two peaks is governed by the distance between the peaks and the width of the bands, and can be defined as... 

CRF-4 is the same as CRF-1 introduced for the simplex, except that the parameter employed for the comparison is the separation parameter S instead of resolution Rs. 

AD, AS, and AR CSPs by adjusting flow rates. The flow rates were varied between 0.5 and 2.0mL/min, but the best resolution was achieved at a flow rate of 0.5 mL/min. Table 5 shows values for separation factor a and resolution Rs of the antifungal agents at flow rates of 0.5 and 1.0 mL/min. There was no resolution for miconazole and sulconazole, while only partial resolution of econazole was obtained when the flow rate was 1 mL/min. Therefore, a... 

Compounds, R Retention factors Separation factor a Resolution Rs... 

Apart from the above-discussed parameters for HPLC optimization of chiral resolution on antibiotic CSPs, some other HPLC conditions may be controlled to improve chiral resolution on these CSPs. The effect of the concentrations of antibiotics (on stationary phase) on enantioresolution varied depending on the type of racemates. The effect of the concentrations of teicoplanin has been studied on the retention (k), enantioselectivity (a), resolution (Rs), and theoretical plate number (N) for five racemates [21]. An increase in the concentration of teicoplanin resulted in an increase of a and Rs values. The most surprising fact is that the theoretical plate number (N) increases with the increase in the concentration of teicoplanin. It may be the result of the resistance of mass transfer resulting from analyte interaction with free silanol and/or the linkage chains (antibiotics linked with silica gel). This would tend to trap an analyte between the silica surface and the bulky chiral selector adhered to it. This is somewhat... 

The basic measure of the efficacy of a single-column chromatographic system in separating two neighbouring peaks can be effected by the resolution (Rs), which is equal to the ratio between the two peak maxima, Afr (distance between the peak centres) and the average base width of the two peaks, as follows (3) ... 

System suitability specifications and tests, Capacity factor (k ), Preci-sion/injector repeatability (RSD), Relative retention (a), Resolution (Rs),Tailing factor (T),Theoretical plate number (N)... 

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