HPLC seperation

Definition and Overview

Chromatography

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Techniques based on the physical the  physical and/or chemical  separation of 2 or more substances in a mixture

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Scope and Purview: -Theoretical Basis -Instrumentation -Qualitative and Quantitative Methods

Chem 221 Instrumental Analysis Spring 2003

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We will focus on Gas Chromatography (GC) but (GC)  but will also make reference to High Pressure Liquid Chromatography  (HPLC)  2

Theory: Basis for Analytical Separations 

The Partition Coefficient (K)

Separations are effected due to differences in differences in substances’ affinities for affinities for a mobile phase and a stationary phase.

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Allows us to quantify the quantify the distribution of a compound between the stationary and mobile phases:

Mobil Mobile e Phase Phase - typically a liquid (LC) or (LC) or a ga a gass (GC)  (GC)  Station Stationary ary Phase Phase - typically solid or solid or a liquid 

K = Cstationary/Cmobile •larg large e K = more time spent in stationary phase

Sample Mixture A B (A & B)

Mobile Phase 

B

= more time spent on the column 

A

increased elution time = larger K 

Stationary Phase Solid Support 3

Sample Chromatogram

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Retention Behavior  tR:

Retention time (thermodynamics) 

•Assume that K is constant for a compound under chromatographic conditions (thermodynamic constant)

Base Peak Width (kinetics) 

Unretained species (K=0)

not a consistent measure of a compound’s relative affinity for stationary and mobile phases -varies with flow rate, temperature, etc.

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Define a new term: Capacity Factor (k’) 

k’ = (tR - tM)/tM = t’R/tM = k’ Adjusted retention Adjusted retention time 5

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Capacity Factor (k’)   

Bandbroadening

Gives a normalized measure of retention Easily calculated from chromatogram Relates directly to the  Partition Coefficient:

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Affects peak width (W)

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Governed by kinetic processes 

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We need to consider the effects of: -Diffusion -Eddy Diffusion -Molecular Diffusion

k’ = K(VS/VM) = nS/nM

-Mass Transfer -time it takes to partition between the stationary and mobile phases

A thermodynamic property.

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Molecular (Longitudinal) Diffusion

Eddy Diffusion 

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Applies only to a column packed with particles (solid support onto which the stationary phase is adsorbed) Each compound species travels a different path  through the particles: 

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Consider the effect of just a solute in a column filled with just mobile phase (no packing) : Mobile Phase

AA AA AA A AA

A AAAAA AAA

Initial  •How affected by:

•How affected by:

Particle Size? Mobile Phase Flow Rate? (↓ as dp ↓)

Mass Transfer

Flow Rate (u)?   (↓ u ↑)

-ALSO: DM varies with mobile phase temp., MW , and viscosity 10

More Mass Transfer

(Stationary Phase) The partitioning process takes time 

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-so, the rate at which a compound partitions  into and out of the stationary phase will affect bandbroadening

Stationary phase mass transfer rate varies with:  DS - stationary phase diffusion coefficient

-increased D S  gives increased rate (decr. broadening)

A A

Diffusion Coeff (D M )? (↑ DM ↑)

(rel. independent) 9

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Final

 K - partition coefficient

-increased K  gives increased rate (decr. broadening)

A

 df

- stationary phase thickness - increased d f  gives decreased rate (incr. broadening)

-A faster partitioning process results in decreased  bandbroadening 11

- mobile phase flow rate - increased u  gives decreased rate (incr. broadening)

u

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Still More Mass Transfer 

Theoretical Plates

Also must consider Mobile-Phase Mass Transfer:

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-varies with only two properties:  DM

Concept derives from distillation theory: 

 The height of a theoretical plate is the length of column  in which the equivalent to a single equilibrium  separation is achieved.

- mobile phase diffusion coefficient

-increased D M  gives increased rate (decr. broadening)

•So, column efficiency  can be gauged by the height of a theoretical plate (H)

 dp - packing particle size

-increased d  p  gives decreased rate (incr. broadening)

•And, the separation power of a column can be assessed by the number of theoretical plates (N), where:

How can we quantify each of these band broadening components?

N = L/H 13

Calculating N  

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The van Deemter Equation

The number of theoretical plates on a column is easily calculated from a chromatogram:

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N = 16 (tR/W)2

Relates column separation efficiency to bandbroadening components as a function of mobile phase linear flow velocity:

H = A + B/u + (CS + CM)u

-assumes that peaks are Gaussian -specific to a particular compound on that column

Eddy Diffusion

•For non-Gaussian peaks (fronted or tailed peaks):

N = 41.7(tR/W0.1)2 1.25 + B/A

Longitudinal (molecular) Diffusion

Asymmetry Ratio (ratio of base widths on either side of maximum)

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The van Deemter Plot

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Resolution •HHPLC ~ 10x smaller than HGC •BUT: NGC > NHPLC

u opt (gives Hmin)

Mass Transfer (stationary and mobile phase)

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This is the most critical figure of merit for a separation . . . How do we define resolution? 

(LGC >> LHPLC) Overall

RS = (2 Z)/(WA+WB)

∆Z = (tR)B - (tR)A

Mass Transfer Eddy Diffusion Longitudinal Diffusion 17

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RS as a Function of Column Properties

RS Values versus Separation 

RS = 0.75

If we:   

RS = 1.0 (4% overlap)

Assume that WA ≈ WB Express RS equation in terms of tR Substitute in k’ and N where appropriate

We obtain: Completely  (baseline)  Resolved 

RS = (N1/2/4) (( - 1)/ ) (k’B/(1 + k’B)

RS = 1.5

α = Selectivity Factor = KB/KA = k’B/k’A = (t’R)B/(t’R)A

(0.3% overlap) 19

N  and t R : Relationships with R S 

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What Do We Want?

We can solve the R S equation for N: 

N = 16 (RS

)2

( /( -

1))2

((k’B +

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1)/k’B)2

The object is to:  Obtain

the MAXIMUM RESOLUTION   In the MINIMUM TIME 

Even more rearranging and substituting allows calculation of the retention time: 

-alas, resolution and time typically work against each other

(tR)B=16(RS)2 ( /( -1))2 ((k’B+1)3/(k’B)2) (H/u )

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Let’s look at how N, k’ and  separation qualities

affect these two

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Effect of Changing N 

Effect of Changing k’ 

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Best resolution is obtained with MAXIMUM number of theoretical plates (RS N1/2)

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How can we increase N?   

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 Resolution 

increases with increasing k’ 

How can we increase k’?  • Recall that k’ is related to the thermodynamics of the partitioning process

• Change:

Optimize mobile phase flow rate (u)  Increase the column length (L) -BUT: both methods also increase the retention time 

Temperature (GC)  Mobile

the height of a theoretical plate (H) -increases column efficiency  -doesn’t sacrifice time (tR H)

 DECREASE 

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phase composition (HPLC)  Stationary phase composition   BUT:

retention time ALSO changes with increasing k’

HOW? 

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The Selectivity Factor (α)

Optimum k’  •How do R S  and t R  vary as a function of capacity factor  (k’) ? •Largest increases in resolution occur with k’1, but also k’ 5 

HPLC: vary mobile phase composition

Temperature

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The General Elution Problem 

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The General Elution Solution! 

How does one resolve ALL compounds in a mixture in which there is a wide range of k’ values?

45 oC

•For GC: dynamically  vary temperature as separation progresses

145 oC

Temperature 

30 - 180 oC

Programming 

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The HPLC Solution

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Instrumentation 

•For HPLC: dynamically vary mobile phase composition as separation progresses

Fairly straightforward:

Gradient  Elution  25 - 400 oC 29

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Mobile Phase Supply & Delivery

Sample Injection

 For GC:  Usually use He or H2 -more efficient at high flow rates than N2

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For GC:

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Syringe/Septum system  At temperature > column temperature  Injection volume: 0.2 - 10 µL  Nanoliter volumes for open  tubular columns 

20 - 100 mL/min flow rates typical -control with flow controller -measure with soap-bubble meter For HPLC:

For

must be degassed and filtered

Sampling

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0.1

- 10 mL/min flow rates typical

HPLC: loop/Injection valve

Injection

PUMP: pulse-free, high-pressure ( 6

volume: 5 - 500 µL

- 10,000 psi) 31

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Nonpolar

Columns 

More Columns!

Size 

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Polar

Stationary

Support

Packed (GC) 1 - 3 meters long 1 - 5 mm I.D. Open Tubular (GC) 10 - 100 meters long 0.1 - 0. 3 mm I.D. HPLC (packed) 100 - 300 mm long 4 - 10 mm I.D.

Packed

High

B.P. (stable at column temps)

(GC)

Glass, Stainless Steel, Copper