3. (a) What are the advantages and disadvantages of using a narrower open tubular column?

(b) What are the advantages and disadvantages of using a longer open tubular column?

(c) What are the advantages and disadvantages of using a thicker film of stationary phase?

(a)

Narrow open tubular columns have greater resolution than wide columns. However, they can accommodate smaller amount of samples and operate at higher pressure.

(b.)

Longer open tubular columns provide greater resolution than shorter columns. This is because resolution is proportional to the square root of the number of theoretical plates, is proportional to column length.

The formula for resolution is described in the expression below:

$\mathrm{Resolution}=\frac{\sqrt{\mathrm{N}}}{4}\times \frac{\mathrm{a}-1}{\mathrm{a}}\times \left(\frac{{\mathrm{K}}_2}{1+{\mathrm{K}}_2}\right)$

where:

$$\begin{gathered} -\mathrm{N}=\mathrm{number}\mathrm{of}\mathrm{plates} \\ -\mathrm{a}=\mathrm{reative}\mathrm{retention} \\ -{\mathrm{k}}_2=\mathrm{retention}\mathrm{factor}\mathrm{of}\mathrm{second}\mathrm{peak}\mathrm{in}\mathrm{pair} \end{gathered}$$

(c)

Using a thicker film of stationary phase increases both the retention time and resolution of early-eluting peaks. The retention factor (k) is described by the expression below:

$\mathrm{k}=\frac{\mathrm{K}}{\mathrm{\beta }}$

The phase ratio can be expressed as the volume of mobile phase over the volume of stationary phase, as shown below:

where:

$$\begin{gathered} -\mathrm{K}=\mathrm{partition}\mathrm{coefficient} \\ -\mathrm{\beta }=\mathrm{phase}\mathrm{ratio} \end{gathered}$$

The phase ratio $\beta$can be expressed as the volume of mobile phase over the volume of stationary phase, as shown below:

$\mathrm{\beta }=\frac{\mathrm{r}}{2{\mathrm{d}}_{\mathrm{f}}}$

where:

$$\begin{gathered} -\mathrm{r}=\mathrm{columm}\mathrm{radius} \\ -{\mathrm{d}}_{\mathrm{f}}=\mathrm{stationary}\mathrm{phase}\mathrm{film}\mathrm{thickness} \end{gathered}$$

Based on the two expressions above, increasing the film thickness decreases the phase ratio $\mathrm{\beta }$. Thus, retention time and sample capacity also increase. With this, the resolution of early-eluting peaks is improved. The thick films of the stationary phase can protect the analytes from the silica surface and reduce tailing. However, at high temperatures, they can aggravate decomposition and evaporation of the stationary phase.