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Performance parameters (Advanced) Theoretical Plate Model

Performance parameters (Advanced) Theoretical Plate Model. Mathematical performance assessment Based on a series of “snapshots” to mimic continuous behaviour Retention time of analyte: t R = t S + t M where t S is the time spent in the stationary phase and rate of movement = 0

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Performance parameters (Advanced) Theoretical Plate Model

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  1. 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

  2. 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

  3. 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)

  4. 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 = t0k = (tR - t0) / t0 K should be between 1 and 5

  5. 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

  6. 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.

  7. 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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