Retention Factor


It is suggested that values of k should be between 2 and 10, but will this work in all cases? If k < 1 separations will be less stable and reproducible. They will have a greater susceptibility to chromatographic interferences at the beginning of the chromatogram, with the chance of peaks being poorly resolved from unretained material at t_{0}. The retention of analytes with low k values will also be more sensitive to small changes in mobile phase composition. However, sometimes a k value of between 1 and 2 may work well when faster chromatography is desired (high throughput), where samples do not contain a lot of endogenous/matrix components or where pH or buffer strength are not vital in controlling retention or selectivity.
For complex mixtures k values greater than 10 may be needed to resolve all peaks. If complex mixtures are being analysed be aware of peak broadening of later eluting peaks that may reduce resolution. 
Real world example
An example in modern chromatography which demonstrates that sometimes larger k values are acceptable, and in this case necessary, in order to generate the required resolution of all 8 components is shown (Figure 1 – 3). At 80 %B (Figure 1) the latest eluting peak has a k of 1.09 and only 3 analytes are fully resolved, reducing the %B to 70% increases the k value to 5, however, there are still only 7 of the 8 compounds resolved (Figure 2). A k of 10 (60% B, Figure 3) is required to fully resolve all 8 compounds.


Figure 1: Separation of 8 nitro compounds.
Column: C18 10 cm x 0.21 cm x 2 µm.
Eluent: Water:MeCN (80% B).
Flow rate: 1.0 mL/min.
Temperature: 35 °C 80% B.
k = 1.09, N = 21629, and R_{s} (min) 0.05. 


Figure 2: Separation of 8 nitro compounds.
Column: C18 10 cm x 0.21 cm x 2 µm.
Eluent: Water:MeCN (70% B).
Flow rate: 1.0 mL/min.
Temperature: 35 °C 80% B.
k = 5, N = 21182, and R_{s} (min) 0.29. 


Figure 3: Separation of 8 nitro compounds.
Column: C18 10 cm x 0.21 cm x 2 µm.
Eluent: Water:MeCN (60% B).
Flow rate: 1.0 mL/min.
Temperature: 35 °C 80% B.
k = 10, N = 21030, and R_{s} (min) 2.03. 

Efficiency


Efficiency can be increased by increasing the column length, reducing the column internal diameter, or decreasing the particle size. It is better to use a smaller diameter packing than increase the column length, which will increase analysis time. However, a decrease in particle size will result in an increase in system backpressure. The use of smaller particles and narrower column internal diameter both require minimized extra column dead volume in order to avoid efficiency losses. 
The FDA stipulates a value for N > 2000 which is typically easily achieved with modern HPLC columns (Table 2).
Column Geometry 
Approximate Efficiency
(Plates, N/column) (V_{εc} – 50 µL) 
250 x 4.6 mm, 5 µm 
22,000 
150 x 4.6 mm, 5 µm 
13,000 
150 x 4.6 mm, 3 µm 
21,000 
100 x 4.6 mm, 5 µm 
9,000 
100 x 4.6 mm, 3 µm 
14,000 
100 x 2.1 mm, 3 µm 
11,000 
100 x 4.6 mm, 1.7 µm 
15,500 
100 x 2.1 mm, 1.7 µm 
23,500 
50 x 4.6 mm, 3 µm 
7,000 
50 x 2.1 mm, 3 µm 
5,500 
50 x 4.6 mm, 1.7 µm 
7,800 
50 x 2.1 mm, 1.7 µm 
11,700 
Table 2: Approximate column efficiencies for standard HPLC column geometries.
A very practical measure of the relative separating power of columns of different dimension is the socalled Resolution Capacity (Table 3).
Column Length, L (mm) 
Particle Size, dp (µm) 
Resolution Capacity L/dp 
300 
10 
30,000 
150 
5 
30,000 
100 
3 
33,300 
50 
1.7 
29,500 
100 
1.7 
58,820 
150 
1.7 
88,230 
Table 3: Resolution Capacity of standard HPLC column geometries. 

Tailing Factor


Tailing peaks create issues with resolution, quantitation (integration), and reproducibility. Peak shape is often the controlling factor when optimising complex separations, especially when components are present in very different concentrations. 


Figure 4: TF = (a) 1.24, (b) 1.42, (c) 1.58
and (d) overlay of a, b, and c. 

Real world example
The analysis of a stability indicating sample at different buffer concentrations demonstrates the importance of the tailing factor (Figure 5 and 6). At a lower buffer concentration (13.4 mM) the degradent peak in the sample has a relatively high tailing factor of 1.72, which although it is in the FDA recommended range, results in poor resolution (R_{s} = 0.98) between the degradent and the proceeding peak. Increasing the buffer concentration (23.6 mM) not only improves the peak tailing of the degradent peak (TF = 1.43) but also results in resolution of the two peaks (R_{s} = 1.69). Note: The retention time of the peaks does not change.


Figure 5: Stability indicating sample (no ionisable compounds), separation previously optimised for selectivity.
Column: C18 10 cm x 0.21 cm x 2 µm.
Eluent: Phosphate buffer (aq):MeOH.
Flow rate: 1.0 mL/min.
Temperature: 35 °C.
Buffer concentration = 13.4 mM. R_{s} = 0.98.
Degradent TF = 1.72. 


Figure 6: Stability indicating sample (no ionisable compounds), separation previously optimised for selectivity.
Column: C18 10 cm x 0.21 cm x 2 µm.
Eluent: Phosphate buffer (aq):MeOH.
Flow rate: 1.0 mL/min.
Temperature: 35 °C.
Buffer concentration = 23.6 mM. R_{s} = 1.69.
Degradent TF = 1.43. 


Precision


Injection precision is important for reproducible chromatographic results and should be estimated in the same way for each analysis. It is indicative of performance of the plumbing, column, and environmental conditions at the time of analysis and assessment of injection reproducibility can be used to aid in the diagnosis of potential system problems such as leaks (Table 4). It is expressed as RSD (relative standard deviation) and is measured by multiple injections of a homogeneous sample (Table 5). Modern autosamplers injection precision is in the range 0.15 – 0.9% (depending on the sample volume).


Sample 
R_{t} 
Peak Area 
Δ R_{t} 
Δ Peak Area 
A1 A2 
5.62 5.66 
2155699 2120466 
0.04 
35233 
B1 B2 
5.87 6.13 
2205659 2288355 
0.26 
82696 
C1 C2 
6.21 6.48 
2227066 2265279 
0.27 
38213 
D1 D2 
6.73 6.99 
2581888 2602016 
0.26 
20128 
Table 4: Injection repeatability data for an HPLC system that developed a leak during sampling.
n 
Mean ± SD 
RSD 
10 
1993162 ± 5029 
0.25% 
Table 5: Representative data for 10 injections
There are several factors that will affect precision which should be considered to minimise errors. 
Chemical factors
 pH/buffer type
 O2 (sample oxidation)
 Light (sample photodegradation)
 Heat (sample thermal degradation)
 Organic components (contaminants, degradation products)
 Mobile phase stability



Facile/Sample handling Issues
 Adsorption to sample containers, syringes, sample loops etc.
 Accurate dilutions
 Thorough sample mixing
 Homogeneous sampling
 Over filled vials (cavitation)
 Emulsions settling over time
 Use of internal standard to estimate loss during sample pretreatment




Resolution


Before setting a value for resolution it is important to ask a couple of questions that relate to the specific separation first:
 What value is acceptable?
 What value is required for reliable quantitation?
Resolution is a function of retention (k), selectivity (α), and efficiency (N) which can all be modified, as has been seen, to improve resolution. R_{s} > 1.5 can often be easily obtained for samples containing 5 or less components, however, for complex mixtures R_{s} > 1.8 is required for rugged performance. ‘Real world’ setting of resolution specifications requires experience in HPLC and the method under consideration. 

