Effect on chromatography of changing
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Learing outcomes.
 Describe the effect on chromatography of changing the column length, phase volume ratio and the partition coefficient.
 Estimated the minimum length of column needed to resolve two components.
Outline of lecture
 Recap of important chromatography terms
 The Craig engine
 Effect of column length
 Effect of partition coefficient and phase volume ratios
 How long should my column be?
Recap of important chromatography terms
In the lecture course separation processes for chemical measurements the following important chromatographic terms were introduced:
Partition coefficient 
Equation 1 

Phase volume ratio 
Equation 2 

Retention factor 
Equation 3 

Number of theoretical plates 
Equation 4 

Height equivalent to a theoretical plate 
Equation 5 Equation 6 
Although we can see how the retention time is predicted to change as the retention factor changes, and intuitively we might estimate that increasing the column length increases the number of theoretical plates and hence the efficiency of the extraction. It is not as easy to visualise how the chromatographic separation changes with these factors. So what does happen when we change:
 the column length?
 the phase volume ratio?; or
 the partition coefficient?
A straight forward visualisation may be obtained from running a simple numerical model known as the Craig engine. The Craig engine is based on a simple plate theory of chromatography. although it is not an accurate representation of the chromatographic process it does give a good feel qualitative feel. It also happens to give the same result as a more rigorous massbalance approach.
The Craig Engine
The Craig engine is a finite element approach, which is a direct analogy of the separation system described by L. C. Craig in 1944, was adopted. The column is divided into n elements. Each element contained a mobile and a stationary phase and analyte moves through the trap from one element to the next. At each timestep, the analyte is equilibrated between the mobile and stationary phases over a period of Dt seconds. This process is represented in Figure 1.
The width of each element, Dz, is determined by the length of adsorbent bed, L.
Dz = L / n 
Equation 7 
The mobile phase velocity, u, is therefore given by
u = Dz / Dt 
Equation 8 
The fraction of the analyte, P, present in the mobile phase after equilibration and hence transferred from one element to the next, is,
P = 1 / ( k´ + 1 ) 
Equation 9 
Thus the concentration of analyte in the mobile phase at element z and time t, Cz,t, can be given in terms of that at time t1 and position z1.
Equation 10 
At every step, some analyte moves down the column in the mobile phase leaving some behind in the stationary phase, and hence dispersion of the analyte will occur asymmetrically.
The dispersion of analyte in an column may also be described by a mass balance equation thus,
Equation 11 
where D is the diffusion coefficient.
If a semiequilibrium model is assumed, where the stationary phase concentration of the analyte is approximately equal to Q, the stationary phase analyte concentration at equilibrium, and k¢ is defined as
k¢ = b ( dQ / dC ) 
Equation 12 
then Equation 12 can be rewritten:
Equation 13 
If diffusion effects are negligible, the right hand side of equation 13 may be set to zero and, in the case of a linear isotherm, the equation can then be solved directly. In the case of a nonlinear isotherm, however, or when diffusion is taken into account, there is no analytical solution. It is possible though to employ iterative methods to achieve a solution.
At low concentrations a type one isotherm is linear, and if diffusion effects are ignored, the differentials in the above equation can be replaced by the following finite difference expressions. For position z and at time t;
Equation 14 

Equation 15 

Equation 16 

Equation 17 
Giving
Cz,t = (1 P) . Cz,t1 + P . Cz1,t1 
Equation 18 
When P = 1 /(k¢ + 1) this is identical to that derived from the Craig model .
 Analyte is introduced to mobile phase element #1.
 Analyte is distributed between mobile and stationary phases according to the Langmuir isotherm.
 Mobile phase moves along adsorbent bed, more analyte introduced to mobile phase element #1.
 Distribution continues along bed.
Effect of column length
The Craig engine model can be used to look at how a chromatographic peak evolves as it progresses further and further down a column. Naturally increasing column length increases retention time. But note that the relationship between retention time and column length is not linear.
Note also how increasing the column length and hence retention time results in the peaks becoming wider and less intense.
Increasing column length therefore:
 increases resolution;
 reduces sensitivity; and
 increases the time required to run the analysis.
So we only increase the length of the column as a last resort. It is better to seek to manipulate the retention factor instead.
Changing the retention factor.
Changing the retention factor involves either changing the nature of the stationary phase to enhance or diminish the strength of interactions between it and the solutes, or changing the amount of stationary phase in the column to alter the phase volume ratio. Whatever approach that is adopted the effect is generally the same. Increasing the retention factor increases the retention time and at the same time is accompanied by a reduction in intensity, and a broadening of the peaks. Increasing the phase volume ratio is a non selective effect and will effect all solutes equally. Changing the nature of the stationary phase, i.e. changing the column will have a selective. Finally the phase volume ratio may be changes through temperature control.
So, control of the retention time is achieved by:
 column length
 mobile phase flow
 type of stationary phase
 phase volume ratio
 and temperature.
the role of the chromatographer is to identify and optimise the best set of conditions to achieve acceptable resolution and sensitivity for a chromatographic separation.