lecture 8 - oct 6
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Lecture 8
Van Deemter Equation!
ResolutionDescribes how well 2 compounds are separated
Rs = 14
N1/2 (-1)k’
1+k’( )efficiency selectivity
retention
k’ = tR-tM
tM
1 < k’ < 10
ResolutionDescribes how well 2 compounds are separated
Rs = 14
N1/2 (-1)k’
1+k’( )N =
L H
Maximize N
LH
L - length of columnCannot increase indefinitely
Limited by:• Long runs times• Back pressure (LC)
Resolution
H - height equivalent of a theoretical plateMeasure of Efficiency
Always want to minimize H• Getting the best performance from system
H depends on:• column parameters• mobile phase• flow rate
Described by Van Deemter
Van Deemter Equation
H B
∞ A + + C
is flow rate
Van Deemter Equation
H
(flow rate)
H B
∞ A + + C
A
C
B
H min
Van Deemter EquationA term
‘Multipath Effect’
Van Deemter EquationA term
‘Multipath Effect’
A ∞ Ce dpCe = particle shapedp = diameter of particle
A term• Entirely dependent on column• Only important in LC
H
(flow rate)
H ∞ A
A
Van Deemter EquationA term
‘Multipath Effect’
Van Deemter EquationB term
‘Longitudinal diffusion’
Van Deemter EquationB term
‘Longitudinal diffusion’
B DMP
∞ DMP = diffusivity of mobile phase
B term• Inversely proportional to flow rate (fast)• Only important in GC (DMP of a gas)
• Typical LC flow rate 0.2-0.5 mL/min• Typical GC flow rate 1-2 mL/min
H
(flow rate)
H B
∞
B
Van Deemter EquationB term
‘Longitudinal diffusion’
Van Deemter EquationC term
‘Mass transfer’
dt = diameter of tubeDMP = diffusivity of MPGC C
dt2
DMP
∞
dp = diameter of particlesDMP = diffusivity of MP = tortuosity
LC C dp
2∞ DMP
Van Deemter EquationC term
‘Mass transfer’
GC C dt
2
DMP
∞
LC C dp
2∞ DMP
Van Deemter EquationC term
‘Mass transfer’
GC C dt
2
DMP
∞
LC C dp
2∞ DMP
Van Deemter EquationC term
‘Mass transfer’
GC C dt
2
DMP
∞
LC C dp
2∞ DMP
H
(flow rate)
H ∞ C
C
Van Deemter EquationC term
‘Mass transfer’
Van Deemter EquationGC
H
(flow rate)
H B
∞ A + + C
A
C
B
H min
X
Van Deemter EquationGC
H
(flow rate)
H B
∞ + C
C
B
H min
dt2
DMP
Van Deemter EquationGC
H
(flow rate)
H DMP
∞ +
C
B
H min
Van Deemter EquationGC
Ideal Column (open tubular):• Small internal diameter (dt)• Use length to increase N (N=L/H)
Ideal Mobile Phase:• High diffusivity to C term and
allow higher flow rates
Van Deemter EquationLC
H
(flow rate)
H B
∞ A + + C
A
C
B
H min
X
Van Deemter EquationLC
H
(flow rate)
H ∞ A + C
A
C
Van Deemter EquationLC
H
(flow rate)
H ∞ +
A
C
dp2
DMP
Ce dp
Van Deemter EquationLC
Ideal Column (packed):• Small particles (dp)• Uniform particles (Ce and )• Cannot use length to increase N
Ideal Mobile Phase:• High diffusivity (DMP) to C term and allow higher flow rates
Dong, M. Today’s Chemist at Work. 2000, 9(2), 46-48.
Van Deemter EquationLC
H ∞ + dp
2DMP
Ce dp
Van Deemter EquationLC
H ∞ + dp
2DMP
Ce dp
Ascentis Express, Supelco, technical information