chapter 22: introduction to analytical …wemt.snu.ac.kr/lecture 2014-1/analytical chem/2014...

Harris: Quantitative Chemical Analysis, Eight Edition

CHAPTER 22:

INTRODUCTION TO ANALYTICAL SEPARATIONS

CHAPTER 22: Opener A

CHAPTER 22: Opener Ba

CHAPTER 22: Opener Bb

CHAPTER 22: Opener Bc

CHAPTER 22: Opener Bd

22-2 What is Chromatography ?

22-2 What is Chromatography ?

Mobile Phase : the solvent moving through the column : either liquid or gas Stationary Phase: the one that stays in place inside the column : most commonly a viscous liquid chemically bonded to the inside of a capillary tube or onto the surface of solid particles packed in the column. Eluent : fluid entering the column Eluate : fluid emerging from the end of the column Packed column : a column filled with particles of stationary phase Open column : a narrow, hollow capillary with stationary phase coated on the inside walls

Principle of Chromatography (1)

Matchbox model of chromatographic separation. Substance A dissolves equally in phase 1 and phase 2, while substance B dissolves 75% in phase 2. continued


22-2 Types of Chromatography

22-2 Types of Chromatography (1)

Chromatogram : a graph showing the detector response as a function of elution time. Retention time ( ): time needed to reach the detector after the injection Adjusted retention time ( ) : additional time required for the solute to travel the length of the column. = - Retention volume ( ): volume of mobile phase required to elute a particular solute from the column

22-3 A plumber’s view of chromatography

rt

rV

rt'

rt' rt mt

U t V flowratevolumevrr )(⋅=

Retention time (tm) : retention time of unretained solvent : time for solute to spend in mobile phase

)phase)( mobile offraction (volumeArea(A))rate(U flow Volume

(m/s) rate flowLinear v

ε×=

Uv : cm3/s A : cm2 ε : dimensionless


Retention factor ( ) : (= Capacity factor ) (= partition ratio)

m

r

m

mrtt'

ttt k =

−=

Relative retention (α) : for any two components 1 and 2,

1

2

r

r

t't' α =

: fairly independent of flow rate : the greater α, the greater the separation between 1&2 : to help identify peaks when the flow rate change


phase mobilein spends solute timephase stationaryin spends solute time =

* The longer a component is retained by the column, the greater is the retention factor

k

m

rmtt

ttt k '=−=

phase mobile in solute of molesphase stationaryin solute of mole

phase mobilein spends solute timephase stationaryin spends solute time ==k

m

s

VV

K ⋅=

Cs : conc. of solute in the stationary phase Cm : conc. of solute in the mobile phase Vs : volume of the stationary phase Vm : volume of the mobile phase K : partition coefficient

mm

ss

VCVC ⋅⋅

=

Only when the column is run slowly enough to be near equilibrium, Cs/Cm = K, the partition coefficient

22-3 Relation Between Retention Time and the Partition Coefficient

Relative retention (α)

1

2

1

2

1

2

1

2

1

2KK

VVK

VVK

kk

ktkt

t't' α

m

sm

s

m

m

r

r =⋅

⋅==

⋅⋅

==

*The relative retention (α) of two solutes 1&2, is proportional to the ratio of their partition coefficients. → physical basis of Chromatography


(Vr) retention volume : volume of mobile phase required to elute a particular solute from the column

(Uv) : volume flow rate of the mobile phase

msm

svmvrr VV K)

VV(KU t U t V +⋅=+×⋅=⋅= 1

m

s

m

r

m

mrVV K

tt

ttt k ⋅=−=

−= 1

mm

sr t)

VV

(K t ⋅+×=∴ 1

Vm

* The retention volume of a particular solute is constant over a range of flow rates


How well are compounds separated by chromatography ? Two factors for estimation : 1) The difference in elution times between peaks ? 2) How broad are the peaks ?

22-4 Efficiency of Separation

22-4 Efficiency of Separation : Resolution

Solute moving through a chromatograph column tends to spread into a Gaussian shape with standard deviation σ

Common measures of breadth : 1) 2)

2/1ww

av

r

av

rrr

wΔt

wΔt

wwtt

2/121

12 589.0

2

peaks twoofResolution ==+−

=

22-4 Efficiency of Separation : Resolution

For quantitative analysis, a resolution > 1.5 is highly desirable.

22-4 Efficiency of Separation : Diffusion


Flux (mol/m2s) = J = - D dc/dx

D (diffusion coefficient) : the rate at which a substance moves randomly from a region of high concentration to a region of lower concentration.

Intervals : 155 mili second (ms)



)2622(2 −= Dtσ

25)-(22 e4

m C 4/x- 2 tD

tD⋅=

π

( ) 3)-4 ( e2

1 y 22 2/-x- σµ

πσ⋅⋅

⋅=

- If the elution time increases by a factor of 4, diffusion will broaden the band by a factor of 2.

- Comparison of Equations 23-25 and 4-3 shows that

The Gaussian Profile of the Band

C: concentration, t: time, x : distance from the current center of the band m: moles of solute that diffuse through a column in an infinitely sharp layer

22-4 Plate Height : A Measure of Column of Efficiency

x Hx )μD (

μxD t D σ

xx

⋅=⋅=⋅=⋅=2222

xμD H, 2height plate = )2722(

2−=

xσ

x : a distance solute has traveled (M) µx : linear flow rate (M/s) H : plate height (M) : height equivalent to a theoretical plate

If solute has traveled a distance x at the linear flow rate of (m/s), Then the time it has been on the column is t = x/ or = x /t

xμ

xμ

The name comes from the theory of distillation in which separation can be performed in discrete stages called plate

xμ

22-4 Plate Height : A Measure of Column Efficiency

*Smaller plate height → narrow peak → better separations → greater number of plates ( N ) in column.

H = 0.1 ~ 1 mm in Gas-chromatography

H = ~ 10 µm in HPLC (High Performance Liquid Chromatography)

H = < 1 µm in capillary electrophoresis

xμD H, 2height plate =

xσ

2

=


HLN =

2

2

2

2

2

16w

LσL

σLx

HLN ==== (unit : length)

2

216w

tN r= (unit : time) tr : retention time of peak (time) w : band width at the base (time)

(L = x, w = 4σ ) L : a column length when solute emerge (length) N : number of theoretical plate in the entire column (dimensionless) w : band width at the base (length) - If N is expressed in time

- For solute emerging from a column length L, the number of plates (N) in the entire column :


22/1

2

22/1

2

22/1

2

2

2 55.555.5)35.2/( w

tw

Lw

LσLN r====

- If w1/2 is used instead of w,

(w1/2 = 2.35σ)

(22-28a)

(22-28b)

N (number of theoretical plates) for the asymmetric peak :

BA w .A/B

/wt.N ..r +=

+ 10

210

)251()(741~


(22-29)

22-4 Factors Affecting Resolution

The greater the resolution the better the separation

30)-(221)-(4

Resolution γN=

N : No. of theoretical plates in the column UA, UB : linear velocities of components A and B

t A, t B : retention times of components A and B

A

B

B tt

UUA

==γ

2

toalproportion is Resolution*

byresolutionincreaseslengthcolumnthedoubling

N

>−

For two closely spaced peaks, the relation between plates and resolution is

Fig.22-15 Separation of 0.5M L-phenylalanine and 0.5M L-phenylalanine-D5 (five deuterium atoms) by repeated pass through a pair of chromatography columns. The mixture is recycled through the same two columns over and over.

The square of resolution is proportional to the number of passes or plate number, N.

22-4 Factors Affecting Resolution

N toalproportion is Resolution*

22-5 Why Bands Spread

- A band of solute invariably spreads apart as it travels through a column

and emerges at the detector with a standard deviation σ.

- The observed variance (σ2obs) = σ1

2 + σ22 + ··· = Σ σi

2

σi2 : the variance from each contributing mechanisms to bands

broadening

* variance is additive but σ is not.

- Variance due to injection : (variance of final bandwidth)

* solute can not be applied to column in an infinitesimally thin zone,

so the band has a finite width even before it begins spreading

∆t : initial bandwidth at injection (measured in time unit)

σinjection2 : final bandwidth

- Variance due to detection :

* a time ∆t is required for the sample to pass through the detector.

12)(Δσ

22injection

t=

12)(σ

22detector

t∆=

22-5 Broadening outside the column

- Over the last 30 years, an enormous amount of theoretical and experimental

effort has been devoted to developing quantitative relationships describing the

effects of experimental variables on plate heights for various types of columns.

- But it is apparent that none of these is entirely adequate to explain the comple

physical interactions and effects that lead to zone broadening and thus lower

column efficiencies.

band thenarrower the H smaller the , xσHheight plate

2>−=

A theory of Band broadening on column

Plate Height Equation

22-5 Broadening inside the column

x : a distance solute has traveled (M)


band thenarrower the H smaller the , xσHheight plate

2>−=

x : a distance solute has traveled (M)

Van Deemter Equation (1950s, Dutch chemical engineer)

xx

CuuBAH ++≈

Multiple paths Longitudinal diffusion Equilibration time

ux : the linear flow rate (mL/min)

A : coefficient of Eddy diffusion (mm)

B : coefficient of Longitudinal diffusion (mm·mL/min)

C : coefficient of mass transfer (mm·min/mL)

22-5 Broadening inside the column : Plate Height Equation

m2DB =

Figure 22-16. Application of Van Deemter Equation to gas chromatography.

xx

CuuBAH ++≈

-This equation tells three mechanisms of band broadening that are : i) independent of flow rate ii) inversely proportional to flow rate and iii) proportional to flow rate, Changing column and stationary phase changes the value of A,B,C

A = 1.65 mm, B= 25.8 mm mL/min C = 0.0236 mm min/mL

The slower the flow rate, the more time is spent on the column and the more longitudinal diffusion occurs.

Solute continuously diffuses away from the concentrated center of its zone.

Why Bands Spread ? : 1) Longitudinal Diffusion

- Solute spreads out along the length of the column – mainly by diffusion

in the mobile phase.

-Solute continuously diffuses away from the concentrated center of its zone.

-The greater the flow rate, the less time is spent on the column and

the less longitudinal diffusion occurs.

Standard deviation of band : tD ⋅= 2σ

xuLDtD ⋅

=⋅=∴ mm

2 22σ

)3422(2σ m2

D −≡==∴xx u

BuD

LH

L : entire column length Dm : solute diffusion coefficient in mobile phase t : detention time HD : plate height due to longitudinal diffusion

the faster ux the less t lower HD

Why Bands Spread ? : 1) Longitudinal Diffusion

m2DB =

Figure 22-17

Why Bands Spread ? : 2) Finite Equilibration Time Between Phases

- Finite time is required for solute to equilibrate between the mobile and

stationary phases.

- However, while some solute is stuck in the stationary phase, the remainder

in the mobile phase moves forward, thereby resulting in spreading of the

overall zone of solute.

k : retention factor d : thickness of stationary phase Ds : diffusion coefficient of solute in the stationary phase r : column radius Dm : diffusion coefficient of solute in the mobile phase

Why Bands Spread ? 2) Finite Equilibration Time Between Phases

xx

CuuBAH ++≈ Equilibration time,

or Mass transfer term

)3522()( transfermass −+== xmsx uCCCuH

)3522()1(3

2

s

2

2s aDd

kkC −+

=

)3522()1(24

1161

m

2

2

2

m bDr

kkkC −

+

++=

Plate height due to finite equilibrium time :

Mass transfer in stationary phase :

Mass transfer in mobile phase :

- If d and r decrease, Hmass transfer decreases.

For gas chromatography in an open tubular column,

Cs is related to the rate of mass transfer through the stationary phase Cm is related to the rate of mass transfer through the mobile phase

Figure 22-19 Analysis time decreased when temperature increased

xx

CuuBAH ++≈

1) Increasing linear flow rate by 5 times decreasing retention time (good) decreasing resolution (bad) due to the increase in Hmass transfer 2) Increasing temperature : Increasing resolution (good) due to the decrease in Hmass transfer (Dm and Ds )

Equilibration time, or mass transfer term

due to the increase in Dm and Ds.

- Because some flow paths are longer than others, molecules entering the column

at the same time on the left are eluted at different times on the right. - The term A is murky because we approximate many different effects by the constan

Why Bands Spread ? 3) Multiple Flow Paths (Eddy Diffusion)

Multiple paths, or eddy diffusion

xx

CuuBAH ++≈

Fig. Open tubular columns. columns : fused silica (SiO2) coated with polyimide, stainless steel, ...

22-5 Advantages of Open Tubular Columns

- For a given pressure, flow rate is proportional to the cross sectional area of the column and inversely proportional to the column length, Q = f (A, L) when P is fixed. - Particles in a packed column resist flow of the mobile phase, so the linear flow rate can not be as fast as the open tubular column. - At a given P and Q, the open tubular column can be made 100 times longer (for example) than the packed column. -If plate height is the same, the longer column provides 100 times more plates, yielding 10 times more resolution.

20)-(231)-(4

Resolution γN=

22-5 Advantages of Open Tubular Columns

* Characteristics of Open Tubular Column 1. Higher resolution: i) H is reduced because no multiple flow path occurs ii) smaller H and longer column due to higher flow rate at the same given pressure provides more theoretical plates. 2. Shorter analysis time 3. Increased sensitivity to small quantities of analyte 4. lower sample capacity not useful for preparative separation

22-5 A Touch of Reality: Asymmetric Bandshapes

i) Ideal isotherm a symmetric peak

ii) Fronting : overloaded column (so much solute applied)

- K=Cs/Cm increases with increasing solute loading.

(“like dissolves like”) the stationary phase resembles solute.

- The band emerges gradually but ends abruptly.

Three common isotherms (Cs vs. Cm ) and their resulting bandshapes

iii) Tailing: a long tail occurs when small quantities of solute are retained

more strongly than large quantities. : Silanization reduces tailing (to prevent hydrogen bonding between polar solute and solid support containing hydroxyl groups)

Three common isotherms (Cs vs. Cm ) and their resulting bandshapes

iv) Distortions of this kind (Fronting and Tailing) is undesirable because they lead to poorer separation and less reproducible elution time.

22-36

chapter 22: introduction to analytical …wemt.snu.ac.kr/lecture 2014-1/analytical chem/2014...

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