chapter 22: introduction to analytical …wemt.snu.ac.kr/lecture 2013_1/analytical chem/2013...

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

O l h ll ill ith t ti h t dOpen 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 1and phase 2, while substance B dissolves 75% in phase 2. continued

22-2 Types of Chromatography

22-2 Types of Chromatography (1)

22-3 A plumber’s view of chromatography

Chromatogram : a graph showing the detector response as a function of elution time.Retention time ( ): time needed to reach the detector after the injectiontRetention time ( ): time needed to reach the detector after the injectionAdjusted retention time ( ) : additional time required for the solute to travel

the length of the column.

rtrt'

= -Retention volume ( ): volume of mobile phase required to elute a particular

l f h lrVrt' rt mt

solute from the columnr UtV flowratevolumevrr )(


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

(m/s) rate flowLinear v

Retention time (tm) : retention time of unretained solventUv : cm3/s A : cm2 : dimensionless

: time for solute to spend in mobile phase


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

1

2

r

r

t't'

α

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

Retention factor ( ) :(= Capacity factor ) m

r

m

mrtt'

ttt k

k

( )(= partition ratio)

mm

phasemobileinspendssolutetimephase stationaryin spends solute time

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

22-3 Relation Between Retention Time and the Partition Coefficient

phasemobileinsoluteofmolesphase stationaryin solute of mole

phasemobileinspendssolutetimephase stationaryin spends solute time k

rmt tttk '

phasemobilein soluteofmolesphasemobilein spends solute time

C : conc of solute in the stationary phasemt

Cs : conc. of solute in the stationary phaseCm : conc. of solute in the mobile phaseVs : volume of the stationary phaseVC

V

s

Vm : volume of the mobile phaseK : partition coefficient

mm

ss

VCVC

m

s

VV

K

O l h h l i l l h bOnly when the column is run slowly enough to be near equilibrium, Cs/Cm = K, the partition coefficient


Relative retention ()Relative retention ()

VK s

1

2

1

2

1

2

1

2

1

2KK

VVK

VK

kk

ktkt

t't' α

sm

s

m

m

r

r

Vm

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


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

(Uv) : volume flow rate of the mobile phase( v) p

mss

vmvrr VV K) VV(KU t U t V 1

mV

m

s

m

r

m

mrVV K

tt

ttt k

1

Vm

mmm Vtt

ms

r t)VV

(K t 1mV

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

22-4 Efficiency of Separation

How well are compounds separated by chromatography ?Two factors for estimation :Two factors for estimation :

1) The difference in elution times between peaks ?2) How broad are the peaks ?) p

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) 2/1ww2) w

22-4 Efficiency of Separation : Resolution

rrrr

wΔt

wΔt

wwtt

2/121

12 589.0 peaks twoofResolution

avav wwww

2/121

2For quantitative analysis, a resolution > 1.5 is highly desirable.

22-4 Efficiency of Separation : Diffusion


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

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


Intervals : 155 mili second (ms)


The Gaussian Profile of the Band

25)-(22 e4

m C 4/x- 2 tD

tD

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

3)-4 ( e2

1 y 22 2/-x-

m: moles of solute that diffuse through a column in an infinitely sharp layer

)2622(2 Dt

2

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

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

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

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

xμμ

xHx)D(xDtDσ 2222

Then the time it has been on the column is t = x/ or = x /txμ xμ

xHx )μ

(μ

Dt D σxx

22

xμD H, 2height plate )2722(

2

xσ

x

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

: height equivalent to a theoretical plate

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

22-4 Plate Height : A Measure of Column Efficiency


DH, 2height plate σ 2

LN xμ

, gpx H

N

*Smaller plate height narrow peak better separationst b f l t ( N ) i l greater number of plates ( N ) in column.

H = 0.1 ~ 1 mm in Gas-chromatography

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

H = < 1 m in capillary electrophoresis


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

2

2

2

2

2

16w

LσL

σLx

HLN (unit : length) (22-28a)

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

If N is expressed in time

2

216tN r (unit : time)tr : retention time of peak (time)w : band width at the base (time)

- If N is expressed in time

2w w : band width at the base (time)

2222 555555 tLLL- If w1/2 is used instead of w,

22/1

2

22/1

2

22/1

2

2

2 55.555.5)35.2/( w

tw

Lw

LσLN r (w1/2 = 2.35) (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

N

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

30)-(221)-(4

Resolution N

BtUA

N : No of theoretical plates in the column

AB tU

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

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

toalproportion is Resolution* N

2byresolutionincreaseslengthcolumnthedoubling

22-4 Factors Affecting Resolution

Fig.22-15 Separation of 0.5M L-phenylalanine and 0.5M L-phenylalanine-D5(fi d i ) b d h h i f h h l(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 NThe square of resolution is proportional to the number of passes or plate number, N.

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 .

- The observed variance (2obs) = 1

2 + 22 + ··· = i

2

i2 : the variance from each contributing mechanisms to bands

broadening

* variance is additive but is not.

22-5 Broadening outside the column

2

- Variance due to injection : (variance of final bandwidth) 12

)(Δσ2

2injection

t

* 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)

injection2 : final bandwidth

- Variance due to detection : 12)(σ

22detector

t

* a time t is required for the sample to pass through the detector.12

22-5 Broadening inside the column

σ2

Plate Height Equation

band thenarrower the H smaller the , xσHheight plate

A theory of Band broadening on column

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

y g

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 complex

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

column efficiencies.

22-5 Broadening inside the column : Plate Height Equation

Van Deemter Equation (1950s, Dutch chemical engineer)

xx

CuuBAH

Multiple paths Longitudinal diffusion Equilibration timeEquilibration time

ux : the linear flow rate (mL/min)

A : coefficient of Eddy diffusion (mm)

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

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

m2 DB

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

xCuuBAH A = 1.65 mm, B= 25.8 mm mL/min

C = 0 0236 mm min/mLxu

Thi ti t ll th h i f

C 0.0236 mm min/mL

-This equation tells three mechanisms of band broadening that are :

i) independent of flow rateii) inversely proportional to flow rate andiii) proportional to flow rate,) p p ,

Changing column and stationary phase changes the value of A,B,Cchanges the value of A,B,C

Why Bands Spread ? : 1) Longitudinal Diffusion

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

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

Why Bands Spread ? : 1) Longitudinal Diffusion

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

in the mobile phase.p

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

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

the less longitudinal diffusion occurs.

Standard deviation of band : tD 2σ

LDtD

m2 2

2

L : entire column lengthDm : solute diffusion coefficient in

mobile phasexu

tD mm

2 2σ

2σ2 BD

mobile phaset : detention timeHD : plate height due to longitudinal

)3422(2σ mD

xx uB

uD

LH

D p g gdiffusion

the faster ux the less t lower HDm2DB

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

Figure 22-17

- 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.

Why Bands Spread ? 2) Finite Equilibration Time Between Phases

xx

CuuBAH Equilibration time,

or Mass transfer termxu

)3522()( transfermass xmsx uCCCuHPlate height due to finite equilibrium time :

F h t h i t b l l

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

)3522()1(3

2 2

2s aDd

kkC

Mass transfer in t ti h

- If d and r decrease, H t f decreases

For gas chromatography in an open tubular column,

)1(3 sDk

)3522()1(24

1161 2

2

2

m bDr

kkkC

stationary phase :

Mass transfer in mobile phase :

Hmass transfer decreases.

k : retention factord : thickness of stationary phase

)1(24 mDk

Ds : diffusion coefficient of solute in the stationary phaser : column radiusDm : diffusion coefficient of solute in the mobile phase

Figure 22-19 Analysis time decreasedh t t i dwhen temperature increased

due to the increase in Dm and Ds.

CuBAH xx

Cuu

AH

E ilib ti ti

1) Increasing linear flow rate by 5 times

Equilibration time,or mass transfer term

1) Increasing linear flow rate by 5 times decreasing retention time (good) decreasing resolution (bad)

due to the increase in Hdue to the increase in Hmass transfer2) Increasing temperature : Increasing resolution (good)

d t th d i Hdue to the decrease in Hmass transfer(Dm and Ds )

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

xx

CuuBAH

- Because some flow paths are longer than others, molecules entering the column Multiple paths, or eddy diffusion

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

22-5 Advantages of Open Tubular Columns

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

- For a given pressure, flow rate is proportional to the cross sectional area of the columnand 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.p

-If plate height is the same, the longer column provides 100 times more plates, yielding 10 times more resolution. 20)-(231)-(

4Resolution N

22-5 Advantages of Open Tubular Columns

* Characteristics of Open Tubular Column1. Higher resolution: i) H is reduced because no multiple flow path occurs

ii) smaller H and longer column due to higher flow rateii) smaller H and longer column due to higher flow rateat the same given pressure provides more theoretical plates.

2. Shorter analysis time3. Increased sensitivity to small quantities of analyte4. lower sample capacity not useful for preparative separation

22-5 A Touch of Reality: Asymmetric Bandshapes

Three common isotherms (Cs vs. Cm ) and their resulting 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)polar solute and solid support containing hydroxyl groups)

22-36

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

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