Chromatographic Theory Prof Examen

8/13/2019 Chromatographic Theory Prof Examen

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Lecture 2. Chromatographic theory.

Chromatographic Theory

Basis of the separation process

Chromatographic separation process is based on the difference in the surfaceinteractions of the analyte and eluent molecules.

Component A: interaction with adsorbent is as strong as for eluent molecules.Component B: strong excessive interaction.

Result:

Component Ais moving trough the column with the same speed as eluentmolecules.

Component Bis moving slower than the eluent flow.

1

AB

B

B

A

AA

A

A

B

B

B

B

B

B

A

A

A


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General scheme of chromatograph instrument.

Chromatogram.

A graphical or other presentation of detector response, concentration of analyte inthe effluent or other quantity used as a measure of effluent concentration versuseffluent volume or time. n planar chromatography !chromatogram" may refer to thepaper or layer with the separated #ones.

$

%luent &an'

(ump

n)ection valve

Column

*etector

(lotter

+raction collector

,etention time

C

A

B


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Band Broadening.

&ypical volume of the sample in)ected is -$/l.

&ypical volume of the sample collected is milliliters.

Broadeningis caused by: the noneven flows around and inside the porousparticles, slow adsorption 'inetics, longitudinal diffusion, and other factors. &helonger the component retained, the more broad its #one.

Separation performancedepends on both component retention and bandbroadening.

Band broadeningis, in general, a 'inetic parameter, dependent on the adsorbentparticle si#e, porosity, pore si#e, column si#e, shape, and pac'ing performance.

Retentiondoes not depend on the above mentioned parameters, but it reflectsmolecular surface interactions and depends on the total adsorbent surface.

&wo approaches can be ta'en to explain the separation process.(late theory 0 proposed in 121 by 3artin and 4ynge. Based on analogy withdistillation and counter current extraction. ate theory 0 accounts for the dynamicsof a separation, introduced by 5.5. 6an *eemter in 1-7.

8


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Retention Parameters.

Retention time,tR the time between the in)ection point and maximum of thedetector response for correspondent compound. etention time is inverselyproportional to the eluent flow rate, FC.

Retention olume,VR the volume of the eluent passed through the column whileeluting a particular component.

c

RR

F

Vt =

!inimum possible retention time, tM0 time of unretained mobile phase to traveltrough the column.

Ad"usted retention time, t'R0 additional time required for solute to travel thelength of the column, beyound the time required by unretained solvent.

t'R = tR- tM

Relatie retention, 0 the ration of the ad)usted retention times of thecomponents.

where t'R29 t'R1, so 91. &he greater is, the greater is separation between twocomponents. elative retention is used to identify the pea's when the flow rate

changes.

Capacity factor, k'0 also called retention factor, capacity ratio, partition ratio.Capacity factor is dimensionless and independent on any geometrical parameters ofthe column. t could be considered to be a thermodynamic characteristic of theadsorbentcompoundeluent system.

2

1

$

1

$

R

R

R

R

t

t

V

V

=

=

M

MR

M

MR

t

tt

V

VV

k

=

=:


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#$ample of calculations.

A mixture of ben#ene, toluene and methane was in)ected into a gas chromatograph.

3ethane gave a sharp pea' in 2$ s, whereas ben#ene required $-1 s and toluenewas eluted in 888 s. +ind the ad)usted retention time and retention factor for eachsolute and relative retention.

S%&'T(%).&he ad)usted retention times are

Ben#ene: t'R; tR0 tM; $-1 0 2$ ; $/ s&oluene: t'R; tR0 tM; 888 0 2$ ; $1 s

&he retention factors are

Ben#ene: k'; tM; 2$ ; -./&oluene: ' ; tM; 2$ ; 7.

&he relative retention is

= t'R(toluene) / t'R(benzene)


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Relation bet-een retention time and partition coefficient.

f the solute is not adsorbed and spend all the time in mobile phase

tR= tMk'; /

f the solute spend equal time in mobile and stationary phases

tR= 2tMk'; 1

n other words,k' (time !olute !pen" in !tationary pha!e) / (time !olute !pen" in mobile pha!e)

f the solute spends#times as much time in in the stationary phase as in the mobile

phase, there will be#times as many moles of solute in the stationary phase as inmobile phase at any time.

or

where Cis concentration, and Vis volume

7

M

MR

M

MR

t

tt

V

VVk

=

=

&ime solute spends in stationary phase

&ime solute spends in mobile phase

moles of solute in stationary phase

moles of solute in mobile phase

k '=C$V$

CMVM


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f column is run in equilibrium conditions

C$/ CM;%

whereKis partition coefficient. (artition coefficients depends on the sorbent,eluent and analyte nature, as well temperature.

elation of retention time to partition coefficient

note: V$/ VM (VR& VM) / VM (tR& tM) / tM

Because ad)usted retention time t'R, retention factor k'and partition coefficientK

are proportional to each other, relative retention can be expressed as:

The relatie retention of t-o solutes is proportional to the ratio of their

partition coefficients.&he greater the ratio of partition coefficients between mobileand stationary phases, the greater the separation between two components of amixture.

?

k '=%V$

VM=

tRtM

tM=

t 'R

tM

=t 'R2

t 'R=

k '$

k '1=

%$

%1


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#$ample of calculations.

etention time of methane tR(methane); 2$ s

etention time of ben#ene tR(benzene); $-1 s

@pen tubular column:nternal diameter of the column: $-/ m.

&hic'ness of stationary phase layer: 1./ m.

%stimate the partition coefficient of ben#ene, and state what fraction of the timeben#ene spends in mobile phase.

S%&'T(%).

Crosssectional area of column ; d$>2 ; 2 ; 2.81/2Dm$

3iddle diameter of coating d; $2 Dm

Crosssectional area of coating ; dthic'ness ; $21./ ; ?.1/$Dm$

Both phases extend for full length of the column, therefore:

64> 63;


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Scaling 'p.

3nalyticalpurposes vs.preparati1epurposes.

%asiest way to achieve this is to 'eep the column length constant and increase thecolumn crosssectional area.

&o reproduce the separation conditions, the linear flow rateshould be 'ept

constant.&hat means, the volume flow rate should be proportional to the column crosssection, and therefore to the mass of analyte.

$ample ma!!

Column 1olume=con!t

ma!!$

ma!!1=

ra"iu!$

ra"iu!1

$

1olume lo/$

1olume lo/1=

ma!!$

ma!!1


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#fficiency of separation.

&wo basic factors: distance between pea's


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1iffusion.

Consider a single band, traveling trough the column.

&he molecules are diffusing across the plane with a concentration gradient d/d!.

+ic's first law of diffusion describes the number of moles crossing each squaremeter per second:

Flu5 molm$! 6=7"c

"5where * id diffusion coefficient.

f the solute was in)ected as infinitely sharp layer with concentration of m

moles>m$, the Faussian profile of the band is:

where tis time, and!is distance along the column from the current center of theband.

&he standard deviation of the band is:

11

c= m

27te

5$

27t

=$7t


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Plate 2eight. Column #fficiency.

&wo approaches can be ta'en to explain the separation process.(late theory 0 proposed in 121 by 3artin and 4ynge. Based on analogy withdistillation and counter current extraction.ate theory 0 accounts for the dynamics of a separation, introduced by 5.5. 6an*eemter in 1-7.

Plate theory. Performance by one pea3.

&he column is considered to be separated on to a number of"late#, on which theequilibrium of the solute with the mobile and stationary phases occurs. &he whole

length of the column is divide by this n$%&erof thetheoretial "late# to give theheiht of the theoretial "late. As many points of equilibrium are in the column,and as narrow they are, as efficient the column is.

(late height is introduced by equation


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Humber of the theoretical plates of the column of)length is given by:

where tRis retention time, and wis pea' broadness in unit! o time.

Ising halfheight width w1/2instead of width at the base:

#$ample:etention time is 2/? s.Base width of the band is 18 s.Column length is 1$.$ m.+ind the number of plates and plate height.

18

#=L

8=L

5

$=

L$

$=17

L$

$

17 tR $

= tR $

#=-.-2- tR1/$$

#=17tR

$

= 17 2/?

$

!

$

18$!$ =1.-?1/2

8=L

#=

1$.$ m

1.-?1/2=/.? mm


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&he real pea's are asymmetric.

Asymmetry factor:

&ailing factor:

Humber of plates:

12

>1/

1>1/ BA

*etector responce

time

3=

>1 /1/ h

31/1/ h

*=3>

$3

#=21.?

>

31.$-

tR $

=21.?

31.$-tR

$


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Resolution.

By convention, resolution


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Relation bet-een plates number and resolution.

esolution is proportional to square root of plates number or column length.

4electivity vs. efficiency:

17

Re!olution=$tR2tR

$1

#=17 tR/ $

tR=#

2 /

Re!olution=

#

2

1

k 'a1

1k 'a1#=#1#$k 'a1=

k '1k '$$

Jow selectivity


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Band broadening outside the column.

&he solute cannot be in)ected as infinitely thin #one. &he band has some finitewidth even before entering the column.

f the band is applied as a plug of width*t, the contribution to the final variance is:

&he broadening in the detector holds the same relationship, because some finitetime is required for the sample to pass trough.

#$ample.

%lution rate is 1.8- ml>min.

w1/2for the collected band is 17.8 s.

6olume of the sample applied is /.8/ ml.

*etector volume is /.$/ ml.

+ind the variances introduced by in)ection and detection. +ind the width at halfheight, which

is caused by column only.

S%&'T(%).

&he observed total variance is:

&he time of in)ection is: *tin+etion; min= ; /.$$$ min ; 18.8 s.

4imilarly, *tdetetor; min= ; . s, and /4detector; 7.- s$.

/4obs /4

column5 /4

detector5 /4

in"ector

/column; -.1? s.

&he width due to column broadening alone is: w1/2; $.8-Gcolumn 1$.1 s.

1?

in@ection$

="etector$

= t

$

1$

ob!$=/1/$$.8-

$

=17.8$.8-$

=2.11!$

in@ection$

= tin@ection

$

1$=

18.8$

1$=12.1!

$


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6an 1eemter #7uation.

&he (late &heory is ta'ing the diffusion as only source of the band broadening.

5.5. 6an *eemter proposed in 1-7 the equation, which ta'es into account threecomponents:

multiple path of an analyte trough the column pac'ingN

molecular diffusionN

effect of mass transfer between phases.

&he plate height is expressed as:

where,is multiple pass term,is longitudial diffusion term, Cis equilibrationtime term, and $!is linear flow rate.

&he most significant result is that we can find an optimum eluent flow rate wherethe column efficiency will be the best.

+or pac'ed columns:3 > CO /

+or opentubular columns:3; /

+or capillary electrophoresis:3 C; /

1

8 3>

u5Cu5


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,term. !ultiple flo- path.

&he velocity of mobile phase in the column may vary significantly across thecolumn diameter, depending on the particle shape, porosity, and the whole bedstructure.

Band broadening due to differing flow velocities can be written in form:

,is theoretical plate height


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Term/$!. !olecular diffusion.

&he molecules disperse or mix due to the diffusion. &he longitudinal diffusion


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Term C$!. #ffect of mass transfer bet-een phases.

4ome finite time is required for solute to equilibrate between the mobile and thestationary phases.

(late height due to finite equilibration time of the mass transfer is:

where C#describe the rate of mass transfer trough stationary phase, and C%describes mass transfer through mobile phase.

&he equations are different for JC an FC.

GC. %pen tubular column.

k'is the capacity factor," is the thic'ness of stationary phase,7!and7mare the diffusion coefficients in stationary and mobile phases,ris column radius.

*ecreasing the stationary phase thic'ness dreduces plate height and increasesefficiency, because solute diffuse faster across the stationary phase.

*ecreasing the column radius rreduces plate height and increases efficiency byreducing the distance trough which the solute must diffuse to reach the stationaryphase.

$1

8ma!! tran!2er=Cu5=C!Cmu5

C!=$ k '

8k '1$

"$

7!

Cm=17 k '11 k '$

$2k '1$

r$

7m


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9inetics of the mass transfer in &C pac3ed column.

3ass transfer for the modern types of pac'ing materials combines two effects: adsorption 'ineticsN mass transfer

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Chromatographic Theory Prof Examen

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