Performance parameters (Advanced)
Theoretical Plate Model
Mathematical performance assessment
Based on a series of “snapshots” to mimic continuous behaviour
Retention time of analyte: tR = tS + tM
where

tS is the time spent in the stationary phase and rate of movement = 0
tM is the time spent in the mobile phase, rate of movement = mobile
phase rate
Each molecule has a chance of being mobile or stationary during any “snapshot”

Distance travelled between periods in the stationary phase = one theoretical plate
Assumes no diffusion in the mobile phase
This gives us simple equations describing chromatographic performance
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Performance parameters (Advanced)
Chromatographic Efficiency
Column Efficiency (measured by plate number: N)
N = (tR/s)2
tR is total retention time, and s is the standard deviation of a gaussian peak
BUT s requires accurate determination of points of inflection, so we use
N= 5.54 x (tR / peak width at 50% height)2
Large N indicates good column performance (should be ~10,000 for HPLC)
N is increased by:
 increased temperature, column length
 decreased stationary phase particle size, flow rate, mobile phase viscosity
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Performance parameters (Advanced)
Chromatographic Efficiency
Other variants of chromatographic efficiency
Effective N (Neff): If tR is low, then t0 affects apparent efficiency
Neff = 5.54 x [(tR - t0) / peak width at half height]2
Plate Height (H): Used to compare columns of different lengths:
H= L / N
L = column length, N = number of plates
H is a measure of plate size, the smaller (lower H) the better (HPLC ~ 10mm)
Effective plate height: takes account of columns with different dead spaces
Heff = L / Neff
Reduced plate height: allows comparison of columns with different particle sizes
h = H / dp
where dP is the particle diameter (same units as L); (Good HPLC column: h = 3)
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Performance parameters (Advanced)
Capacity Factor (k)
The ratio of mass in the stationary phase (mS) to that in the mobile phase (mM)
where total mass: mT = mM + mS
Capacity Factor: k = mS / mM
= K. (VS / VM)
where K is the equilibrium constant, VS is the volume of the stationary phase, and
VM is the volume of the mobile phase (dead volume).
Determining k
Assume VR : VM = mT : mM
Then: VR / VM = mT / mM = (mM + mS) / mM
=1+k
So:
VR = VM (1 + k)
And:
tR = tM (1 + k)
Since tM = t0
k = (tR - t0) / t0
K should be between 1 and 5
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Performance parameters (Advanced)
Selectivity (α) and Resolution (Rs)
Selectivity Factor (α): Comparison of interaction with stationary phase
Ratio of capacity factors


α = k (B) / k (A)
Primarily affected by changing the stationary or mobile phases
Larger α means better separation (but little gain in resolution beyond α=3)
Resolution (RS): A measure of how well separated two peaks are:
RS = 2(tR peak A - tR peak B) / (wA + wB)
Since measuring w is difficult, can use:
RS = 0.25 x [(α - 1) / α] x [ k(B) / (1 + k(B)) x N
where B is the last eluting peak, and N is the plate number for B
High Rs is better: should be at least 1.5 for baseline separation
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Performance parameters (Optimisation)
Optimisation depends on type of chromatography, usually involves changes in:

Stationary Phase: Hundreds of kinds on offer, choice based on analytes to
be separated, cost Differences based on chemical structure, particle size,
column bore and length, compressibility of packing

Mobile Phase: Use changes in polarity, pH, viscosity

Detector: Use best sensitivity available for analytes

Flow rate: affects retention time and diffusion and thus performance



Amount of sample: Too much will overload the column, too little will be
difficult to detect accurately
Sample Matrix: Avoid incompatible contaminants, use minimum injection
volume, preferable similar to the mobile phase (HPLC)
Temperature: increases improve performance (must avoid decomposition of
sample) by increasing solubility and reducing viscosity. Very important in GC.
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Performance parameters (Summary)
Chromatographic systems must be optimised to give:

Good Peak Shape

Good separation/resolution (N, k, α, Rs)

Flat and horizontal baseline

No “artifactual” peaks

Shortest possible analysis times
Resolution and Retention time are key
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