Figure 4.15
Efficiency as a function of mobile phase velocity
and the effect of each term in equation (4.46).efficiencies are achieved with stationary phases of small particle size (small values of A and C ) and
thin coatings of liquid (small value of C ). In practice, the choice of operating conditions is often a
semi-empirical one based on previous experience. Equation (4.46) applies strictly to packed column gas
chromatography (p. 97) but similar equations have been derived for capillary column gas
chromatography (p. 99) and for high performance liquid chromatography (p. 118).
A more fundamental equation for resolution than equation (4.45) is given by the expression
where N 2 is the efficiency (plate number) measured for the second solute, k 2 is its retention factor and α
is the separation factor defined as k 2 /k 1. An Rs value of 0 indicates that the two solutes are completely
unresolved and would occur if α were 1 (i.e. when k 1 = k 2 ), or if k 2 were 0 (i.e. if the second solute
eluted on the solvent front (p. 85). Improvement in the resolution of two solutes can be achieved by
increasing the magnitude of one or more of the three terms in equation (4.47) which are essentially
independent variables. The first term is affected by particle size, column length and flow rate (p. 86 et
seq.) but it should be noted that a doubling of resolution requires a fourfold increase in efficiency. The
second and third terms are affected by the nature of the mobile and stationary phases, temperature and
pressure. Very significant improvements in resolution can often be achieved by changing one or both of
the phases as this can have a large effect on the value of α, especially if it is initially very close to 1.
Although resolution increases significantly with increasing k 2 for early-eluting peaks, once k 2 gets much
larger than 10, further improvement is negligible because the third term rapidly approaches 1.