Kinetic Optimization of Speed and Efficiency in Fast Ultra-High Resolution HPLC M.M. Dittmann (1), K. Choikhet (1), G. Desmet (1) (1) Agilent Technologies, Waldbronn, Germany () Vrije Universeit, Brussels, Belgium Page 1
Introduction The kinetic plot model (KPM) has been extensively used to investigate performance of columns based on efficiency and permeability mainly on isocratic separations. The first part of this presentation will demonstrate how the model can be extended to allow the optimization of gradient separations a a function of column performance and compound retention parameters In the second part the model was used the investigate the influence of extra column contribution - in particular the influence of connection capillary diameter - on kinetic performance. Page
Column Performance Characteristics H-u curve Line Chart Column: Agilent SB-C18 RRHD.1x5 mm P vs. u curve Scatter Plot HETP [um] 9.5 9 8.5 8 7.5 7 6.5 6 5.5 A4.4 B 5 C.8 Pressure e drop [bar] 1 1 8 6 4 Φ 5 5 4.5 4 4 6 8 1 1 14 linear velocity [mm/s]..4.6.8 1 1. 1.4 linear velocity (cm/s) N (column length, flow rate) Column permeability Overall column performance through kinetic plot method Page 3
Kinetic Plot Optimization for isocratic elution Find L* and N* corresponding to a given t and P max over a large range of t L * ΔP P d max η Φ p t * N * * L H ( u * ) u * ΔP max d η Φ t p experimental HETP equation Page 4
Isocratic Kinetic Plots t vs. N for 1.8 µm Particles Scatter Plot Temperature (C) - 3 Temperature (C) - 8 35 3 5 15 1 5 Pmax 55 bar Pmax 11 bar 5 5 75 1 15 5 5 75 1 15 Plate Number N Each data point corresponds to a different column length operated at maximum pressure Page 5
Kinetic Plots for Gradient Separation In gradient separation the resolution is determined not only by the column plate number but also by the gradient steepness. Resolution in gradient separation is usually expressed as Peak capacity P c Maximum Peak Capacity (Rs 1) without sample imposed limit Maximum Peak Capacity (Rs 1) with sample imposed limit P 1 + c t g 4σ P 1 + c t r t, last r. first 4σ σ t (1 + k ( t) e N ) k 1 e b t R t t + t D + ln( b ( k' start t D / t ) + 1) b t S Δφ t b t *P.J. Schoenmakers et al, JCA, 149, 519, (1978) g Page 6
Variation of Peak Capacity with Gradient Time Line Chart Line Chart 6 4 Column length: 1 mm Flow rate:.8 ml / min 34 34 7 S 6.5 ln k,1 ln k, 6 19 17 15 Peak Capac city 18 16 14 1 Sample independent Δ Retention time 34 164 13 95 13. 11. 9.3 7.3 5.4 4 sigma [s s] 1 6 3.4 8 Sample dependent 5-1 1.4 -.5 5 1 15 5 3 35 tg (s) 5 1 15 5 3 tg (s) Δ t R t b b( k' / ) + 1 last td ln b( k' first td / t ) + 1 t Page 7
Kinetic Plots for Various Gradient Slopes Scatter Plot Temperature (C) - 3 Temperature (C) - 8 5 Retentio on time of las st peak 175 15 15 1 75 5 5 5 1 15 5 1 15 PC column Peak Capacity t /t g. t /t g 5.5 t /t g. t /t g 1.1 Page 8
Kinetic Plots for fixed Column Length (@ 3 C) Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 5 45 L 3 mm Retent tion time of last peak 4 35 L 5 mm 3 L 1 mm 5 15 L 15 mm 1 5 4 6 8 1 1 14 16 4 6 8 1 1 14 16 Peak Capacity Peak capacity (column) Page 9
Flow Rate Ranges in Fast Gradient LC @ 3 C for.1 mm column Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 45 15 mm F < 1 ml/min 4 F 1 ml/min Retentio on time of la ast peak 35 3 5 15 1 1 mm 75 mm 5 mm 75 mm 1 mm 15 mm F > ml/min 5 3 mm 5 mm 3 mm 4 6 8 1 1 14 16 4 6 8 1 1 14 16 Peak Capacity Peak capacity (column) Page 1
5 5 Flow Rate Ranges in Ultra-Fast Gradient LC @ 8 C for.1 mm columns Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 1 mm 75 mm 1 mm F < 1 ml/min t peak 175 5 mm 75 mm F 1 ml/min F > ml/min Retention n time of last 15 15 1 75 3 mm 3 mm 5 mm 5 5 4 6 8 1 4 6 8 1 Peak Capacity Peak capacity (column) Page 11
Experimental Determination of Peak Capacity P c 1+ t t r, last r. first 4σ t marker First Peak 4 σ Last Peak Page 1
Rete ention time [ min] System: Sample: Column: Gradient: Page 13 14 Experimental Peak Capacity Data Temperature - 3 Binned StartPressure - x 7 Scatter Plot Temperature - 3 Binned StartPressure - 7 < x 16.8 ml/min 1 1 8 6 4 16 14 1 1 8 6 4.8 ml/min 1.6 ml/min Temperature - 8 Binned StartPressure - x 7 Temperature - 8 Binned StartPressure - 7 < x.7 ml/min 1.4 ml/min 15 1.5 ml/min 5.5 ml/min 6 7 8 9 1 11 1 13 14 15 6 7 8 9 1 11 1 13 14 15 Peak PC Capacity Agilent 19 Infinity Alkylphenones, Thiourea, Acetanilide, Benzophenone Agilent RRHD SB-C18 1% - 9% Acetonitrile.1 x 5 mm.1 x 1 mm
Fast Gradient Runs PC 85 t /t g.3 PC 8 t /t g.4 PC 79 t /t g.5 PC 67 t /t g.75 System: Agilent 19 Infinity Sample: Alkylphenones, Thiourea, Acetanilide, Benzophenone Column: Agilent RRHD SB-C18.1x5 mm Flow rate:.5 ml/min (~ 11 bar max. Pressure) Gradient: 1% - 9% Acetonitrile Temperature: 8 C Page 14
Kinetic Plots Including External Band-Broadening Basic relationships Pressure drop in a packed column Pressure drop in connection capillaries (F volumetric flow rate) (Poiseuille flow) Δ P packedcolumn kd u η L F η L col col Kt rcolπ εt Kt ΔP P opentube F 8η Lcap 4 r π cap F η L F 8η L col cap Δ P total 4 r π ε K + r π col T t cap insert L col t F r π ε col T F η ( r π ε ) col t T K t + F 8η L π r cap 4 cap ΔP total Solve for F, determine L Page 15
Setup of Low Dispersion System for Determination of Capillary Variance 45 nl injection loop.75 x 1 mm PEEK-coated FS capillary Part to be investigated (column, capillary, HE etc.).5 x 1 mm FS-Capillary CE-XXCell (13 nl cell volume) Page 16
Experimental Determination of Capillary Variance σ V, Capillary Line Chart r 4 cap L Cap 4 D π F m Golay equation 6 rimental σ [μl ] expe 5 4 3.17 x 4 mm σ V, Capillary r 4 cap L Cap π const F 4 D m.3 empirical equation Variance.1 x 4 mm 1.85 x 4 mm..4.6.8 1 Flow Rate [ml/min] Page 17
Determination of total System Variance ( + F, N t 1 k' e ) σ V column σ V, Capillary r 4 cap L Cap 4 D π F m Golay equation σ V, Capillary r 4 cap L Cap π const F 4 D m.3 Empirical equation to fit data σ σ + σ total col capillary Page 18
Peak Dispersion in System Capillaries 7 7 6 6 5.6 ml/min 5.6 ml/min signal 4 3.4 ml/min.3 ml/min signal 4 3.4 ml/min.3 ml/min. ml/min.1 ml/min 1.55 ml/min 5 1 15 Elution Volume [µl]. ml/min 1 5 1 15 Elution Volume [µl].1 ml/min.5 ml/min.17 x 15 mm.17 x 4 mm J.G. Atwood, M.J.A. Golay, JCA, 18, 97(1981) Page 19
Kinetic Plots including External Contributions (.1x3 mm Column) @ 3 C Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 1 t peak Retention n time of las 8 6 4 4 6 8 1 1 4 6 8 1 1 Peak Capacity Peak capacity (system) Page
Kinetic Plots including External Contributions (.1x5 mm Column) @ 3 C Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 18 16 Retentio on time of la ast peak 14 1 1 8 6 4 4 6 8 1 1 14 4 6 8 1 1 14 Peak Capacity Peak capacity (system) Page 1
Kinetic Plots including External Contributions (.1x15 mm Column) @ 3 C Scatter Plot Pmax system (bar) - 55 Pmax system (bar) - 11 9 8 t peak Retention n time of las 7 6 5 4 3 1 8 1 1 14 16 18 4 8 1 1 14 16 18 4 Peak capacity Capacity (system) Page
Conclusions The kinetic plot model cannot only be used to compare isocratic performance of different columns but it can potentially ti be used on a much broader scale in method development This method can be employed to optimize separations in gradient mode based on column performance, retention parameters and extra-column contributions. The kinetic plot model as well as the experimental data suggest that for ultra-fast gradient separations the best performance / time is achieved well above the minimum of the van Deemter curve with flow rates in the range of 1 3 ml/min at high pressures and temperatures Page 3
Acknowledgements Ken Broekhoven Jeroen Billen Deirdre Cabooter Vrije Universiteit of Brussels Page 4