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Two Solutes The separation ratio of two solutes (A) and (B), (aA/B), is taken as the ratio of their corrected retention volumes, i.e.,                                       The separation ratio is simply the ratio of the solute distribution coefficients which depends only on the operating temperature and the chosen phase system. Most importantly, they are independent of both the mobile phase flow rate and the phase ratio of the column. Thus,  the same separation ratio for two solutes would be obtained from either a packed column or a capillary column if the same temperature and the same phase system is used (at this time no exclusion effects from the support or stationary phase is assumed). To identify a solute, a standard substance is added to the sample mixture and the separation ratio of the

Phase Van Deemter derived the following expression for the variance contribution by the resistance to mass transfer in the mobile phase, (), (6)   where (k') is the capacity ratio of the solute, and the other symbols have the meaning previously ascribed to them. The Resistance to Mass Transfer in the Stationary Phase Dispersion due to resistance to mass transfer in the stationary phase is exactly analogous to that in the mobile phase. Solute molecules close to the interface will leave the stationary phase and enter the mobile phase before those that have diffused further into the stationary phase and have a longer distance to diffuse back. Thus, as those molecules that were close to the surface will be swept along in the moving phase, they will be dispersed from those molecules still diffusing to the surface. The dispersion resulting from the resistance to mass

. It is also seen from equation (8) that the optimum velocity is a function of the capacity ratios (k') of the solutes separated. A graph relating the function of (k') that determines the magnitude of the optimum velocity and the capacity ratio is shown in figure 18.   It is seen that the highest optimum velocities are realized for solutes eluted close to the column dead volume so that for very fast separations the stationary phase should be chosen to elute the solutes below a capacity ratio of 2. However, the curve flattens at a (k') value of about 4, and subsequently the optimum velocity remain constant and is virtually independent of the capacity ratio of the eluted solute  

It is seen that for the column 100 mm in diameter and 30 m long, the resistance to mass transfer in the gas phase is at least 20 times that in the stationary phase and this smallest value only occurs at low capacity ratio values (ca. one or less) and very low mobile phase exit velocities (ca 0.5 cm/s.). Capillary columns are rarely operated at exit velocities of less than 20 or 30 cm/s. and at such velocities, the resistance to mass transfer in the stationary phase is less than 2% of the total resistance to mass transfer and this is still at a (k') value of unity. It follows that for this column, the dominant resistance to mass transfer dispersion effect occurs in the mobile phase, except possibly at (k') values close to zero (when the solute is eluted close to the dead volume of the column). Consequently, under most conditions used in practice, the resistance to mass transfer in the mobile phase will be the controlling effect on peak dispersion. &

diffusivity of the solute in the mobile phase, measured at atmospheric pressure and (g) is the inlet/outlet pressure ratio of the column.   A description of the various dispersion processes that take place in a column are given in book 9 of this series. In the case of the capillary column the first expression in equation (2) describes the effect of longitudinal diffusion, the second expression described the effect of the resistance to mass transfer in the mobile phase and the last expression the resistance to mass transfer in the stationary phase.   It is interesting to estimate the relative magnitude of the two components of the resistance to mass transfer by examining the ratio of the resistance to mass transfer in the mobile phase to that in the stationary phase, i.e., (3)   In order to evaluate equation (3) for any given column and phase system the relationship between (h) and (uo) needs to be identified.  

calculate how the ratio of the two mass transfer coefficients changes with the mobile phase exit velocity (uo) for columns of different length and radii. Two columns were examined, one 30 m long and 100 mm I.D. and the other 15 m long and 300 mm I.D. Each column was examined for solutes having capacity ratios of 1, 5, and 20 (i.e. k=1, 5 and 20). Helium was assumed to be the carrier gas and the diffusivity of the solute in the gas phase (Dm) taken as 0. 4 sq. cm/sec. and that in the stationary phase (Ds), 2.5 x 10-5 sq. cm/sec.. The film thickness (df) was taken in all examples to be a mean value of 0.2 mm. The results obtained are shown as curves relating the log(mass transfer ratio) to the mobile phase exit velocity for each of the four capacity ratio (k') values in figure 15.