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van Deemter metrics: Ø Plate height (h) Ø Mobile phase velocity (ν)
h = A + B /ν + C ⋅ν
Practically meaningful metrics: Ø Plate count (N) Ø Plate count per unit time (N/t0)
Pmax = 400 bar, T = 40 oC, φ = 500, 2.1 mm i.d. A = 1.0, B = 5.0, C = 0.05 , ε e = 0.38, ε i = 0.30 Dm = 1 × 10-5 cm2/sec, η = 6.6 × 10-4 Pa/sec
Poppe plot allows fair comparison under optimized conditions!!!
Response
80
t0 = 0.50 min tR = 2.19 min N = 26,500 tR = 3.68 min N = 26,000 tR = 6.63 min N = 25,000
Halo C18 (F = 0.52 ml/min)
1 2
Analytical Development, AstraZeneca Pharmaceuticals Department of Chemistry, University of Minnesota
HPLC 2009, Dresden, 1 July 2009
Pharmaceutical and Analytical R&D 1 1 July 2009
2
van Deemter optimum 1.8 µ m Point L (cm) ν F (ml/min) ∆P (bar) 1 5 10 0.44 282 13,900 13.4 1037 3.5 µ m 2 5 10 0.23 38 7,100 26.1 272 51% 26%
2
1
N
1.8 µm 3.5 µm
Higher Efficiency
Poppe, H., J. Chromatogr. A 1997 , 778, 3-21
Why compared with Poppe plot?
Van Deemter optimum
-2.0 -2.2 -2.4 log(t 0/N) -2.6 -2.8 -3.0 -3.2 1 s -3.4 3.0 3.5 4.0 log(N) 10 s 10 s
Which one gives better performance?
Fully porous Sub-2 µm 0.5 µm sub-2 µm fully porous particles at 1000 bar 2.7 µm superficially porous particles at 600 bar Superficially porous 2.7 µm
-1.0 -1.5 log(t0/N) -2.0 -2.5 -3.0 -3.5 2.5 1s 10 s
dp = 3.5 µm
10 s
P < 400 bar t0 = 30 sec L = 17.3 cm F = 0.68 mL/min N = 23,900 P > 400 bar
2
10 s
3
t0 = 104 sec L = 316 cm F = 0.04 mL/min N = 221,500
2
Cunliffe et al . J. Sep. Sci. 2007, 30, 3104-3109
Outline
Ø Isocratic Poppe plot • Metrics: efficiency vs. separation speed • Identify optimal operating conditions Ø Performance comparison under isocratic conditions • van Deemter flow studies • Theoretical isocratic Poppe plots • Experimental measurement Ø Gradient peak capacity Poppe plot comparison Ø Conclusions
Faster Separation
t0 = 1 sec L = 3.2 cm F = 3.72 mL/min N = 1,500
4
3.0
3.5
4.0 log(N)
4.5
5.0
5.5
Pmax = 400 bar, T = 40 oC van Deemter equation A = 1.0, B = 5.0, C = 0.03 Dm = 1 × 10-5 cm2/sec η = 6.6 × 10-4 Pa/sec φ = 500, ε e = 0.38, ε i = 0.30
BEH 6.32 0.66 10.24 0.095 2.67
In reduced van Deemter plot: Ø Smaller B term on the Halo phase (less longitudinal diffusion) Ø Smaller C term on the Halo phase (better mass transfer???) Ø Smaller hmin on the Halo phase (< 2 on a 2.1 mm)
t0 2 * ∝ Cd p N lim
-3.5 3.5 4.0 4.5 log N 5.0 5.5
Higher Efficiency
Curve a Curve b
1.7 um BEH at 950 bar 2.7 um Halo at 570 bar
A 0.66 0.78
B C 10.2 0.095 5.73 0.049
6
Experimental design
Sub-2 µm fully porous particle BEH C18 at 950 bar vs. 2.7 µm superficially porous particle Halo C18 at 570 bar
Step 1: Flow study on both columns with alkylphenones Step 2: Transform the results into a theoretical Poppe plot
Step 3: Test the accuracy of the method experimentally. 5cm, 10cm, 15cm, 30cm(2 x 15cm), 45cm(3 x 15cm) Step 4: Extend to gradient elution of pharmaceutical compounds
Ø Halo and BEH give similar performance at short t0 (e.g. < 30 s) Ø Halo gives better efficiency as t0 increases
9
Experiment – Fast separation (5 cm)
Response
3
Isocratic Poppe plot
For any particle size at certain maximum pressure and column dead time, there is optimum column length and flow rate that gives the highest N
vs.
Ø Which one performs better under optimized conditions Ø Relative performance as a function of separation goal • Fast separation • Slow separation
DeStefano et al . J. Chromatogr. Sci. 2008 , 46, 254-260
t0 = 0.08 min
80 60 40 20 0.0 0.2 0.4 0.6
Halo C18 (F = 1.50 ml/min)
tR = 0.27 min N = 5,800
tR = 0.44 min N = 5,900
tR = 0.77 min N = 6,000
1.0 min
0.8 Retention time
Critical Comparison of Performance of Sub-2 µm Particles and Superficially Porous Particles under Optimized Ultrahigh Pressure Conditions
Xiaoli Wang 1, Yu Zhang 2, Partha Mukherjee 1, Patrik Petersson 1
7
van Deemter flow studies – h vs. ν
6 5 4 3 2 1 0 5 10 15 20 25 Reduced Velocity BEH C18 Halo C18
Acquity UPLC, 40 oC
Reduced plate heBiblioteka Baidught
Halo k' A B C hmin 6.22 0.78 5.73 0.049 1.84
Poppe optimum 1.8 µ m 3 5.96 11.9 0.52 400 16,400 13.4 1224 3.5 µ m 4 16.2 32.2 0.73 400 16,700 26.1 640 102% 52%
2 4 1 3 1.8 µm 3.5 µm
4.5 5.0
∆P (bar) N t0 (sec) N/t0 %N % N/t0
8
Theoretical isocratic Poppe plot
-1.5
102 s
103 s
Limiting efficiency
-2.0 log (t0/N)
a N
* lim
∝
d2 p B
Faster Separation
-2.5
10 s
b T = 21 oC
-3.0
Limiting speed
4.5 5.0
t0 (sec) N/t0 %N % N/t0
Pmax = 400 bar, T = 40 oC, φ = 500, 2.1 mm i.d. A = 1.0, B = 5.0, C = 0.05 , ε e = 0.38, ε i = 0.30 Dm = 1 × 10-5 cm2/sec, η = 6.6 × 10-4 Pa/sec
30
20
1.5 min
0.5 1.0 1.5 Retention time
10 0.0
N % Ratio (Halo/BEH)
10
F(mL/min) 140%
t0 (sec) 61%
N/t0 157%
96%
Experiment – Normal separation (15 cm)
Acquired Tuesday, July 22, 2008 10:09:51 AM
5
Why compared with Poppe plot?
Poppe optimum
-2.0 -2.2 -2.4 log(t 0/N) -2.6 -2.8 -3.0 -3.2 1 s -3.4 3.0 3.5 4.0 log(N) 10 s 10 s
2
van Deemter optimum 1.8 µ m Point L (cm) ν F (ml/min) 1 5 10 0.44 282 13,900 13.4 1037 3.5 µ m 2 5 10 0.23 38 7,100 26.1 272 51% 26%
Acquired Thursday, June 26, 2008 5:43:02 PM
Response
40
t0 = 0.11 min tR = 0.46 min tR = 0.75 min N = 5,800 N = 6,200 tR = 1.32 min N = 6,300
BEH C18 (F = 1.07 ml/min)
h = A + B /ν + C ⋅ν
Practically meaningful metrics: Ø Plate count (N) Ø Plate count per unit time (N/t0)
Pmax = 400 bar, T = 40 oC, φ = 500, 2.1 mm i.d. A = 1.0, B = 5.0, C = 0.05 , ε e = 0.38, ε i = 0.30 Dm = 1 × 10-5 cm2/sec, η = 6.6 × 10-4 Pa/sec
Poppe plot allows fair comparison under optimized conditions!!!
Response
80
t0 = 0.50 min tR = 2.19 min N = 26,500 tR = 3.68 min N = 26,000 tR = 6.63 min N = 25,000
Halo C18 (F = 0.52 ml/min)
1 2
Analytical Development, AstraZeneca Pharmaceuticals Department of Chemistry, University of Minnesota
HPLC 2009, Dresden, 1 July 2009
Pharmaceutical and Analytical R&D 1 1 July 2009
2
van Deemter optimum 1.8 µ m Point L (cm) ν F (ml/min) ∆P (bar) 1 5 10 0.44 282 13,900 13.4 1037 3.5 µ m 2 5 10 0.23 38 7,100 26.1 272 51% 26%
2
1
N
1.8 µm 3.5 µm
Higher Efficiency
Poppe, H., J. Chromatogr. A 1997 , 778, 3-21
Why compared with Poppe plot?
Van Deemter optimum
-2.0 -2.2 -2.4 log(t 0/N) -2.6 -2.8 -3.0 -3.2 1 s -3.4 3.0 3.5 4.0 log(N) 10 s 10 s
Which one gives better performance?
Fully porous Sub-2 µm 0.5 µm sub-2 µm fully porous particles at 1000 bar 2.7 µm superficially porous particles at 600 bar Superficially porous 2.7 µm
-1.0 -1.5 log(t0/N) -2.0 -2.5 -3.0 -3.5 2.5 1s 10 s
dp = 3.5 µm
10 s
P < 400 bar t0 = 30 sec L = 17.3 cm F = 0.68 mL/min N = 23,900 P > 400 bar
2
10 s
3
t0 = 104 sec L = 316 cm F = 0.04 mL/min N = 221,500
2
Cunliffe et al . J. Sep. Sci. 2007, 30, 3104-3109
Outline
Ø Isocratic Poppe plot • Metrics: efficiency vs. separation speed • Identify optimal operating conditions Ø Performance comparison under isocratic conditions • van Deemter flow studies • Theoretical isocratic Poppe plots • Experimental measurement Ø Gradient peak capacity Poppe plot comparison Ø Conclusions
Faster Separation
t0 = 1 sec L = 3.2 cm F = 3.72 mL/min N = 1,500
4
3.0
3.5
4.0 log(N)
4.5
5.0
5.5
Pmax = 400 bar, T = 40 oC van Deemter equation A = 1.0, B = 5.0, C = 0.03 Dm = 1 × 10-5 cm2/sec η = 6.6 × 10-4 Pa/sec φ = 500, ε e = 0.38, ε i = 0.30
BEH 6.32 0.66 10.24 0.095 2.67
In reduced van Deemter plot: Ø Smaller B term on the Halo phase (less longitudinal diffusion) Ø Smaller C term on the Halo phase (better mass transfer???) Ø Smaller hmin on the Halo phase (< 2 on a 2.1 mm)
t0 2 * ∝ Cd p N lim
-3.5 3.5 4.0 4.5 log N 5.0 5.5
Higher Efficiency
Curve a Curve b
1.7 um BEH at 950 bar 2.7 um Halo at 570 bar
A 0.66 0.78
B C 10.2 0.095 5.73 0.049
6
Experimental design
Sub-2 µm fully porous particle BEH C18 at 950 bar vs. 2.7 µm superficially porous particle Halo C18 at 570 bar
Step 1: Flow study on both columns with alkylphenones Step 2: Transform the results into a theoretical Poppe plot
Step 3: Test the accuracy of the method experimentally. 5cm, 10cm, 15cm, 30cm(2 x 15cm), 45cm(3 x 15cm) Step 4: Extend to gradient elution of pharmaceutical compounds
Ø Halo and BEH give similar performance at short t0 (e.g. < 30 s) Ø Halo gives better efficiency as t0 increases
9
Experiment – Fast separation (5 cm)
Response
3
Isocratic Poppe plot
For any particle size at certain maximum pressure and column dead time, there is optimum column length and flow rate that gives the highest N
vs.
Ø Which one performs better under optimized conditions Ø Relative performance as a function of separation goal • Fast separation • Slow separation
DeStefano et al . J. Chromatogr. Sci. 2008 , 46, 254-260
t0 = 0.08 min
80 60 40 20 0.0 0.2 0.4 0.6
Halo C18 (F = 1.50 ml/min)
tR = 0.27 min N = 5,800
tR = 0.44 min N = 5,900
tR = 0.77 min N = 6,000
1.0 min
0.8 Retention time
Critical Comparison of Performance of Sub-2 µm Particles and Superficially Porous Particles under Optimized Ultrahigh Pressure Conditions
Xiaoli Wang 1, Yu Zhang 2, Partha Mukherjee 1, Patrik Petersson 1
7
van Deemter flow studies – h vs. ν
6 5 4 3 2 1 0 5 10 15 20 25 Reduced Velocity BEH C18 Halo C18
Acquity UPLC, 40 oC
Reduced plate heBiblioteka Baidught
Halo k' A B C hmin 6.22 0.78 5.73 0.049 1.84
Poppe optimum 1.8 µ m 3 5.96 11.9 0.52 400 16,400 13.4 1224 3.5 µ m 4 16.2 32.2 0.73 400 16,700 26.1 640 102% 52%
2 4 1 3 1.8 µm 3.5 µm
4.5 5.0
∆P (bar) N t0 (sec) N/t0 %N % N/t0
8
Theoretical isocratic Poppe plot
-1.5
102 s
103 s
Limiting efficiency
-2.0 log (t0/N)
a N
* lim
∝
d2 p B
Faster Separation
-2.5
10 s
b T = 21 oC
-3.0
Limiting speed
4.5 5.0
t0 (sec) N/t0 %N % N/t0
Pmax = 400 bar, T = 40 oC, φ = 500, 2.1 mm i.d. A = 1.0, B = 5.0, C = 0.05 , ε e = 0.38, ε i = 0.30 Dm = 1 × 10-5 cm2/sec, η = 6.6 × 10-4 Pa/sec
30
20
1.5 min
0.5 1.0 1.5 Retention time
10 0.0
N % Ratio (Halo/BEH)
10
F(mL/min) 140%
t0 (sec) 61%
N/t0 157%
96%
Experiment – Normal separation (15 cm)
Acquired Tuesday, July 22, 2008 10:09:51 AM
5
Why compared with Poppe plot?
Poppe optimum
-2.0 -2.2 -2.4 log(t 0/N) -2.6 -2.8 -3.0 -3.2 1 s -3.4 3.0 3.5 4.0 log(N) 10 s 10 s
2
van Deemter optimum 1.8 µ m Point L (cm) ν F (ml/min) 1 5 10 0.44 282 13,900 13.4 1037 3.5 µ m 2 5 10 0.23 38 7,100 26.1 272 51% 26%
Acquired Thursday, June 26, 2008 5:43:02 PM
Response
40
t0 = 0.11 min tR = 0.46 min tR = 0.75 min N = 5,800 N = 6,200 tR = 1.32 min N = 6,300
BEH C18 (F = 1.07 ml/min)