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High Performance Liquid Chromatography

Fundamentals - Theory

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to the educational community and

is willing to provide access to

company-owned material.

This slide set is created by Agilent Technologies. The

usage of the slides is limited to teaching purpose only.

In case pictures, sketches or drawings should be used

for any other purpose please contact Agilent

Technologies a priori.

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Introduction

High-performance liquid chromatography (HPLC; formerly referred to as

high-pressure liquid chromatography), is a technique in analytical chemistry

used to separate components in a mixture, to identify each component, and

to quantify components.

HPLC relies on pumps to pass a pressurized liquid solvent containing the

sample mixture through a column filled with a solid adsorbent material. Each

component in the sample interacts slightly differently with the adsorbent

material, causing different flow rates for the different components and

leading to the separation of the components as they flow out the column.

Source: Wikipedia

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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

• Selectivity – Example 2

• Selectivity – Example 3

• 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 What happens inside the column?

tr2-tr1

Superior separation Inferior separation

Superior separation Inferior separation

Wb1 Wb2 Wb1 Wb2

vs

vs

tr2-tr1

ToC

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Time t

Separation tr2-tr1

Peak width Wb1,2

Introduction What happens inside the column?

Resolution describes the ability of a

column to separate the peaks of

interest.

Resolution describes whether you

have achieved base line separation or

not.

ToC

)(2/1 12

12

bb

rrs

WW

ttR

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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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Rs 14

N

a 1

a

k

1k

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

tN r

2

16

b

r

W

tN

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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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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

VS

Ftk

`

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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

ka

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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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How to Influence Separation?

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.

How to Influence Separation?

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

N4

1~Rs

p

c

dh

L4

1~H

L4

1~R cs

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How to Influence Separations?

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

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How to Influence Separations? Bringing It Together – Peak Width and Reduced Height of a Theoretical Plate

h: reduced height of a theoretical plate

ToC

)WW(2/1

ttR

1b2b

2r1rs

p

cs

dh

L4

1~R

)w(fh

)www(fh Caxeddy

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Van Deemter Equation 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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Van Deemter Equation 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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Van Deemter Equation “Resistance to Mass Transfer”

wC ~ dp2

Different diffusion paths

Porous particle

Stationary layer of mobile phase

ToC

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Van Deemter Equation

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

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Van Deemter Equation R

ed

uce

d h

eig

ht o

f a

th

eo

r. P

late

(h)

Flow

Sum curve: Van Deemter

Axial diffusion

Eddy diffusion

Resistance to mass transfer

h = A + B/u + C u

ToC

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Van Deemter Equation 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

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Van Deemter Equation Real Curves for Different Analytes

P. Petersson et al (AZ), J.Sep.Sci, 31, 2346-2357, 2008

• Van Deemter equation for isocratic runs only

• Compound and instrument specific

• Even for sub-2-μm particles not horizontal

• Optimum flowrate depends on compound

ToC

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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(fh 2

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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 The Meaning

“… using the statistical theory of peak overlap …”

“… peak resolution is severely compromised when the number of components present in a sample overrates 1/3 of the peak capacity.”

J.M. DAVIS, J.C. GIDDINGS, ANAL. CHEM. 55 (1983) 418

“…in order to resolve 98% of the components, the peak capacity must exceed the number of components by a factor of 100.”

J.C. GIDDINGS, J. CHROMATOGR. A 703 (1995) 3

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

t1P G

av

G

n

1

G

w

t1

wn

1

t1P

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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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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

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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 andrea_zenker@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

Article reprint A simple approach to performance optimization in HPLC and its application in ultrafast

separation development

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

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ToC

THANK YOU

Publication number 5991-5411EN

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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