5991-5411EN_Agilent_LC_Theory_English.pptx

For teaching purpose only
January 4, 2023
© Agilent Technologies, Inc. 2016
1
BUILDING
BETTER SCIENCE
AGILENTAND YOU
High Performance
Liquid Chromatography
Fundamentals - Theory

January 4, 2023
2
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educational community and is willing to provide
access to company-owned material contained
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This slide set is created by Agilent Technologies. The usage of the slides is
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incurred by Agilent as a result of your use or reproduction of these materials.
In case pictures, sketches or drawings should be used for any other purpose
please contact Agilent Technologies a priori.

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3
Introduction
High-performance liquid chromatography (HPLC) is a standard technique in
analytical chemistry to separate, identify and/or quantify compounds that are
dissolved in a solution.
HPLC instruments consists of a pump, an injector, a separation column and
a detector. An aliquot of the sample is injected onto the column. Each
compound in the sample interacts slightly differently with the column
material, and therefore, causing different flow rates for the different
components and leading to the separation of the components.

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Table of Content (ToC)
Introduction
• What happens inside the column?
Key Parameters
• Retention Time & Peak Width
• Resolution – Baseline Separation
• Resolution – The Fundamental Equation
• Efficiency or Number of Theoretical Plates
• Retention Factor
• Selectivity or Separation Factor
How to Influence Selectivity?
• Selectivity – Example 1
• Plate Number
Van Deemter Equation
• Eddy Diffusion
• Axial Diffusion
• Resistance to Mass Transfer
• More on Van Deemter
Peak Capacity
• Gradient Analysis
• Definition
• Calculation of Peak Capacity
• Peak Width
• Example

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Introduction
What happens inside the column?
Time t
Separation tr2-tr1
Peak width Wb1,2
ToC

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Introduction
tr2-tr1
Superior separation Inferior separation
Superior separation Inferior separation
Wb1 Wb2
Wb1
Wb2
vs
vs
tr2-tr1
ToC

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Introduction
ToC
)
(
2
/
1 1
2
1
2
b
b
r
r
s
W
W
t
t
R




Resolution describes the ability of a
column to separate the peaks of
interest.
Resolution describes whether you
have achieved base line separation or
not.
Time t
Separation tr2-tr1
Peak width Wb1,2

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Key Parameters
Retention Time & Peak Width
tr1
tr2
Wb1 Wb2
W1/2
h
t
tri Retention time
compound i
W1/2 Peak width at half
height
Wbi Peak width at baseline
ToC

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Key Parameters
Resolution – Baseline Separation
Resolution describes the ability of a
column to separate the peaks of interest.
Resolution takes into consideration
efficiency (N), selectivity (a) and
retention (k).
• A value of 1 is the minimum for a
measureable separation to occur and to
allow adequate quantitation.
• A value of 0.6 is required to discern a
valley between two equal-height peaks.
• Values of 1.7 or greater generally are
desirable for rugged methods.
• A value of 1.6 is considered to be a
baseline separation and ensures the most
accurate quantitative result.
h
t
Rs = 1.5
ToC

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10
Rs  1
4
N 
a 1
a






k
1k






Key Parameter
Resolution – The Fundamental Equation of (U)HPLC
Selectivity
Efficiency Retention
One can improve resolution by improving any of these parameters:
• Selectivity has the highest influence on the resolution. Small changes
in selectivity lead to big hanges in resolutions.
• Retention has only a significant influence at small k-values.
• Efficiency describes the separation power of the column.
ToC

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Key Parameter
Resolution – The Fundamental Equation of (U)HPLC
The figure explains resolution as a function of selectivity, column efficiency
or retention.
ToC
Selectivity impacts resolution most
• Change stationary phase
• Change mobile phase
Plates are easiest to increase

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Key Parameter
Efficiency or Number of Theoretical Plates (N)
Column efficiency is used to compare the performance of different columns.
It is expressed as the theoretical plate number, N.
Columns with high plate numbers are more efficient. A column with a high N
will lead to narrower peak at a given retention time than a column with a
lower N number.
Parameters influencing column efficiency:
• Column length (increasing colum length increases efficiency)
• Particle size (decreasing particle size increases efficiency)
ToC
2
2
/
1
54
.
5 









W
t
N r
2
16 









b
r
W
t
N

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Key Parameter
Retention Factor (k)
k =
tr -t0
t0
æ
è
ç
ö
ø
÷
The retention factor measures the time that the sample component resides
in a stationary phase relative to the time it resides in the mobile phase. It is
calculated from the retention time divided by the time for an unretained
peak (t0).
Parameters influencing retention factor:
• Stationary phase
• Mobile phase
• Gradient slope*
• System dwell volume*
*gradient elution only
ToC

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14
The equation shows how the retention factor is influenced by flow rate (F),
gradient time (tG), gradient range (ΔΦ), and column volume (Vm).
Remember: To keep the retention factor constant, changes in the
denominator need to be offset by proportional changes in the numerator,
and vice versa.
Key Parameter
Retention Factor (k) – Gradient Elutions
ToC
m
G
V
S
F
t
k





`

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Key Parameter
Selectivity or Separation Factor (α)
Selectivity is a measure of the time or distance between the maxima of two
peaks. If α = 1, the two peaks have the same retention time and co-elute. It
is defined as the ratio in capacity factors.
Parameters influencing retention factor:
• Stationary phase
• Mobile phase
• Temperature
ToC
a Selectivity
k1 Retention factor of 1st peak
k2i Retention factor of 2nd peak
1
2
k
k

a

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Key Parameter
Influence of N, α, and k on Resolution
ToC

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How to Influence Separation?
Same sample, analyzed with different stationary phases but always same
temperature, mobile phase and gradient.
ToC

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Same sample, analyzed with same stationary phase and temperature but
with different mobile phases (same gradient).
ToC

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Same sample, analyzed with same stationary and mobile phase, same
gradient but different temperatures.
ToC

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How to Influence Separations?
What is a “plate” in HPLC?
A theoretical plate is the hypothetical stage in which two phases of a
substance (its liquid and vapor phase) establish an equilibrium.
ToC
LC Column length
dp Particle size
h Reduced height of a theoretical plate
N
4
1
~
Rs
p
c
d
h
L
4
1
~

H
L
4
1
~
R c
s

January 4, 2023
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High plate number (N) provides:
• Sharp and narrow peaks
• Better detection
• Peak capacity to resolve complex samples
But resolution increases only with the square root of the plate number.
• RS ~ N
Plate number increase is limited by experimental conditions
• Analysis time, pressure
ToC

January 4, 2023
22
Bringing It Together – Peak Width and Reduced Height of a Theoretical Plate
h: reduced height of a theoretical plate
ToC
)
W
W
(
2
/
1
t
t
R
1
b
2
b
2
r
1
r
s




p
c
s
d
h
L
4
1
~
R

)
w
(
f
h 
)
w
w
w
(
f
h C
ax
eddy 



January 4, 2023
23
Eddy Diffusion
weddy ~ λ dp λ: Quality of column packing
Differences in diffusion paths due to:
Different paths Poor column packing Broad particle size
distribution
ToC

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Axial or Longitudinal Diffusion
Increase in peak width due to self-diffusion of the analyte
At low flow the analyte remains in the mobile phase for a long time
• High increase in peak width
• Increased height of a theoretical plate
Flow
ToC

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“Resistance to Mass Transfer”
wC ~ dp
2
Different diffusion paths
Porous particle
Stationary layer of mobile phase
ToC

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26
The Van Deemter equation relates the variances per unit length of a
separation column to the linear mobile phase velocity by considering
physical, kinetic and thermodynamic properties of a separation (Wikipedia).
h = f ( weddy + wax + wC )
h = A + B/u + C u
• Eddy diffusion
• Diffusion coefficient
• Resistance to mass transfer
ToC

January 4, 2023
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Reduced
height
of
a
theor.
Plate
(h)
Flow
Sum curve: Van Deemter
Axial diffusion
Eddy diffusion
Resistance to mass transfer
h = A + B/u + C u
ToC

January 4, 2023
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Measured for Different Particle Sizes
5.0 m
3.5 m
1.8 m
ToC
• Small particles lead to
lower heights of
theoretical plates and
therefore higher
separation efficiency
• For smaller particles
the separation
efficiency suffers less
when increasing the
flow
• Compound and
instrument specific
• Optimum flowrate
depends on
compound

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Isocratic run:
Peak width depends on diffusion processes only.
Gradient run:
Peak width depends on diffusion processes and gradient focusing on the
column head.
Peak Capacity
Gradient Analyses
ToC
Reduced height of theoretical
plate as function of peak width
)
w
(
f
h 2


January 4, 2023
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Peak capacity is the number of peaks (n) that can be separated in a given
time with a given resolution.
The peak capacity depends on different factors like column length and
particle size.
Peak Capacity
Definition
Peak capacity: 32 peaks in 2.5 min
ToC

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Peak Capacity
Calculation of Peak Capacity
Simplification:
ToC
wav Average peak width
n Number of peaks
tG Gradient time
w Peak width of selected peak
w
t
1
P G


av
G
n
1
G
w
t
1
w
n
1
t
1
P 





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Peak Capacity
Peak Width
Peak width according to tangent method
Peak width at half height
Peak width at 5 % height
Peak width at 4.4 % height (5σ)
ToC

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33
Peak Capacity
Example
min
20 40 60 80 100
mAU
0
10
20
30
40
50
min
10 20 30 40 50
mAU
0
20
40
60
Column: 2.1 x 150 mm, 1.8 µm
Back pressure: 402 bar
Peak capacity: 313
Column: 2.1 x 300 mm*, 1.8 µm
Back pressure: 598 bar
Peak capacity: 406
*300 mm column by coupling two 150 mm columns
ToC

January 4, 2023
34
Further Information
For more information on products from Agilent visit www.agilent.com or
www.agilent.com/chem/academia
Have questions or suggestions to this presentation?
Contact academia.team@agilent.com
Publication Title Pub. No.
Primer The LC Handbook 5990-7595EN
Application note
The influence of silica pore size on efficiency, resolution and loading in Reversed-
Phase HPLC
5990-8298EN
Application note Increasing resolution using longer columns while maintaining analysis time 5991-0513EN
Poster
Study of physical properties of superficially porous silica on its superior
chromatographic performance
Application note
Maximizing chromatographic peak capacity with the Agilent 1290 Infinity LC system
using gradient parameters
5990-6933EN
Application note Maximizing chromatographic peak capacity with the Agilent 1290 Infinity LC 5990-6932EN
Application note Increased peak capacity for peptide analysis with the Agilent 1290 Infinity LC system 5990-6313EN
Web CHROMacademy – free access for students and university staff to online courses
ToC

January 4, 2023
35
ToC
THANK YOU
Publication number 5991-5411EN

January 4, 2023
36
Abbreviations
Abbreviation Definition
α Selectivity
dp Particle size
ΔΦ Gradient range
F Flow rate
h Reduced height of a theoretical plate,
a measure of the resolving power of
a column
k Retention factor (formerly known:
k` - capacity factor)
Lc Column length
λ Quality of column packing
N Efficiency or column plate number
P Peak capacity
R Resolution
Abbreviation Definition
t Time
tr Retention time
t0 Column dead-time
tG Gradient time
Vm Colum volume
w Peak width
W1/2 Peak width at half height
Wbi Peak width at baseline
weddy Eddy diffusion
wax Axial or longitudinal diffusion
wC Resistance to mass transfer
wav Average peak width
ToC

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