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Title: An%20Introduction%20to%20Chromatographic%20Separations

An Introduction to Chromatographic Separations
  • Lecture 36

  • Dividing both nominator and denominator by kB
  • R (N1/2/4)(1 kA/kB)/(1kB)/kB
  • However, a kB/kA
  • R (N1/2/4)(1 1/a) (kB)/(1kB)

  • Therefore, resolution can be viewed as a
    composite contribution of three terms
  • a.       Efficiency term where R is proportional
    to N1/2
  • How to increase efficiency?
  • 1. Increase column length as N L/H

  • 2. Decrease H
  •  a. In liquid chromatography
  • Resistance to mass transfer terms (K2 ds2 V/Ds
    and K3 dp2 V/DM) are most important in liquid
    chromatography and thus should be particularly
    minimized. This can be done by
  • Decreasing particle size
  • Decreasing the thickness of stationary phase
  • Working at low flow rates
  • Increase DM by using mobile phases of low

  •  a. In gas chromatography
  • Longitudinal diffusion term (k1DM/V) is the most
    important one in gas chromatography. Reducing
    this term involves
  • Working at higher flow rates
  • Decreasing DM by using carrier gases of higher

  • b.      Retention term where R is proportional to
    k/(1k) which suggests that the retention
    parameter should be optimized. A value for k in
    the range from 5-10 is preferred as smaller
    values (low retention) results in bad resolution
    while a very high k value means very long
    retention with exceedingly small improvements in

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These data can be better viewed as a plot where
as k was increased, almost a plateau was

  • The overlap of two Gaussian peaks of equal area
    and amplitude, at various values of resolution
    (R) is presented below
  • (1) R 0.50                                   
  • Overlap of two peaks 16
  • (2) R 1.00                         
  • Overlap of two peaks 2.3 
  • (3) R 1.50
  • Overlap of two peaks 0.1
  • c.       Resolution is dependent on a selectivity
    term (a 1)/a). As the selectivity is
    increased, resolution increases as well. When a
    1, resolution is zero.

  • When a is close to unity, optimising k' and
    increasing N is not sufficient to give good
    separation in a reasonable time. In these cases,
    a is increased by one of the following
  • 1.      Changing mobile phase composition
  • 2.      Changing column temperature
  • 3.      Changing composition of stationary phase
  • 4.      Using special chemical effects (such as
    incorporating a species which complexes with one
    of the solutes into the stationary phase or use
    of surfactants)

Effect of Other Parameters on Resolution
  • a. The resolution of a column is proportional to
    the square root of its length since N L/H.
  •  LA/LB RA2/RB2
  • b. Retention time as related to resolution can be
    obtained by the following treatment
  • N L/H
  • tM NH/u

  • tR,B tM (1kB)
  • tR,B (NH/u) (1kB)
  • N 16R2(1 kB)/kB2a /(a - 1)2
  • Substitution gives
  • tR,B (16R2H/u)(1 kB)3 /kB2a /(a - 1)2
  • Therefore, one can also write
  • tR,A/tR,B RA2/RB2

  • To obtain a high resolution, the three terms must
    be maximized. An increase in N, the number of
    theoretical plates can simply be done by
    lengthening the column. This leads to two
    opposing effects where resolution is increased
    but at the same time this causes an increase in
    retention time and thus increased band
    broadening. In addition, a longer column may not
    always be available. An alternative is to
    increase the number of plates, the height
    equivalent to a theoretical plate by adjusting
    elution variables (mobile phase composition), and
    other factors affecting selectivity.

Chromatographic Relationships
  • It is often found that by controlling the
    capacity factor, k', separations can be greatly
    improved. This can be achieved by changing the
    temperature (in Gas Chromatography) or the
    composition of the mobile phase (in Liquid

The General Elution Problem
  • Look at the chromatogram below in which six
    components are to be separated by an elution

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Qualitative Analysis
  • Usually, the retention time of a solute is the
    qualitative indicator of a specific analyte. The
    retention time of an analyte is thus compared to
    that of a standard. If both have the same
    retention time, this may be a good indication
    that the identity of the analyte is most probably
    that of the standard. However, there can be
    important uncertainties since some different
    compounds have similar retention. In such cases,
    it is not wise to use the retention time as a
    guaranteed marker of the identity of compound,
    except in cases where the sample composition is

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