Column hold-up volume

RPC separations of ionic samples usually require ionic additives to the mobile phase, which may cause problems in HPLC/MS operations. Completely ionized solutes are much less retained than the corresponding uncharged species and elute close to the column hold-up volume, often as asymmetric or even split peaks. Weak acids are eluted in order of decreasing constants and weak bases... 

FIGURE 5.4 Effect of the gradient dwell volume, V7>. the elution volume, Vj, in reversed-phase chromatography. Solute neburon, retention equation (Equation 5.7) with parameters a=A, m = 4. Linear gradients 2.125% methanol/min (a) from 57.5% to 100% methanol in water in 20min ( i = 50) (b) from 75% to 100% methanol in water in 11.75 min (k = 10). Vg uncorrected calculated from Equation 5.8, Vg + Vg, Vg, added to Vg uncorrected, Vg corrected calculated from Equation 5.21. (A) A conventional analytical C18 column, hold-up volume y ,= ImL flowrate l.OmL/min. (B) A microbore analytical C18 column, hold-up volume y = 0.1mL flow rate 0.1 mL/min. 

If a column with different diameter, but the same length is used, the column hold-up volume changes in proportion to the second power of the column diameters. To keep the separation time constant, the flow rate of the mobile phase should be adjusted in the proportion of changing V , see Equation 5.28. Another possibility of compensation is by adjusting the gradient time to keep the ratio VJitQ-FJ constant [8,9]. 

The effect of the dwell volume on the retention times of analytes increases with decreasing retention factor at the start of gradient elution and with increasing ratio VpIV, and becomes very significant in the instrumental setup with the dwell volume comparable to or larger than the column hold-up volume, which is more likely to occur in micro- or in capillary LC than in conventional analytical LC (see Figure 5.4) [12]. 

Gritti, F., Martin, M., and Guiochon, G. (2005). Influence of pressure on the properties of chromatographic columns. II. The column hold-up volume. J. Chromatogr. A 1070 13-22. 

Fig. I.l. Evaluation of the releniion data from a chromatogram. EmfEo) column hold-up volume, i.e.. the volume of the mobile phase in the column measured as the elution volume of a non-relained solute imdo) column hold-up time VRiffRi) and VriUrj) retention (elution) volumes (times) of retained sample...

NC = no change j = a factor < f L = column length r/,- - column diameter N = column plate number / , = resolution V , = column hold-up volume k = retention factor /k = retention time (proportional to the run time) F = flow rate of the mobile pha.se

mean diameter of packing particles Ap = pressure drop across the column. 

The contribution of the initial isocratic elution step to the total retention volume of the solute is equal to Fr. The part of the column hold-up volume F ,i through which the solute has migrated at the end of the isocratic step, i.e., at the time when it is taken by the front of the gradient is related to the total column hold-up volume in the same proportion as the gradient dwell volume is to the (hypothetical) elution volume from the column under initial isocratic conditions with the retention volume of the solute, Ai, and for the gradient-elution step thus remains only available the hold-up volume F ,2 = F , - F,n. ... 

Here Qt and Qi+1 are the amounts of compound adsorbed by the column packing after the /. th and the (/ + l) th step, when in equilibrium with the concentrations C, and Ci+U respectively. VR,i+ is the retention volume of the inflection point of the (/ +l) th breakthrough curve, VT is the total dead volume (including column void volume, V0), and Vs is the volume of the stationary phase [109], In frontal analysis two different dead volumes must be determined, namely the traditional column hold-up volume, V0, which is used to calculate the volume of the stationary phase, Vs. The other dead volume is the total one, VT, i.e., the entire volume after the T-connector (including V0) and the FA raw-data should be corrected for VT. 

Not only variations in the pressure at constant temperature influence column-to-column retention data the role of the column hold-up volume as well as the mass of stationary phase present in the column is also important. The net retention volume caleulated from the adjusted retention volume corrects for the column hold-up volume (see Table 1.2). The specific retention volume corrects for the different amount of stationary phase present in individual colunms by referencing the net retention volume to unit mass of stationary phase. Further correction to a standard temperature of 0°C is discouraged [16-19]. Such calculations to a standard temperature significantly distort the actual relationship between the retention volumes measured at different temperatures. Specific retention volumes exhibit less variability between laboratories than other absolute measures of retention. They are not sufficiently accurate for solute identification purposes, however, owing to the accumulation of multiple experimental errors in their determination. Relative retention measurements, such as the retention index scale (section 2.4.4) are generally used for this purpose. The specific retention volume is commonly used in the determination of physicochemical properties by gas chromatography (see section 1.4.2). 

To be correct the terms in the brackets should be activities and not concentrations, also, two of the terms involve stationary phase activities that cannot be easily evaluated. The weight distribution coefficient for the sample ion A is given by Da = [As ] / [Am ] and is related to the chromatographic retention factor for the sample ion by Ra = Daw / Vm, where w is the weight of stationary phase and Vm is the column hold-up volume. Substituting these terms into Eq. (4.22) after rearrangement, we have... 

Here, k is the retention factor in a binary mobile phase containing solvents A and B, which can be calculated from the retention volume of the analyte, Vr, and the column hold-up volume, Vm (determined as the elution volume of a nonretained compound, such as trichloroethylene), k = Vr/Vm — 1, fea is k in pure weak solvent. A, o is the activity of the adsorbent in the column. As is the specific surface of the adsorbent, and Sa and Sab are the solvent strength (polarity) parameters of the weak (nonpolar) solvent and of the mixed binary mobile phase, respectively. 

In this, we use the fundamental parameters of the kinetic and thermodynamic theory of chromatography plate number N, column hold-up volume Vj, and retention factor k. They all determine the peak volume, which is crucial for the concentration at the peak summit. Substituting Eq. 2.24 into 2.23, solving for and... 

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