Chapter 26Chapter 26

An Introduction to An Introduction to Chromatographic Chromatographic

SeparationsSeparations

What is chromatography? What is chromatography?

• The separation of a mixture of compounds based The separation of a mixture of compounds based upon the differential partitioning of various analytes upon the differential partitioning of various analytes species between a mobile phase and a stationary species between a mobile phase and a stationary phasephase. .

What is chromatography? What is chromatography?

What is chromatography? What is chromatography?

Chromatogram a plot of analyte signal as a function of elution timeChromatogram a plot of analyte signal as a function of elution time

Classification of Column Classification of Column Chromatographic Methods Chromatographic Methods

The Effect of Migration Rates and Zone The Effect of Migration Rates and Zone Broadening on Resolution Broadening on Resolution

The Effect of The Effect of Migration Migration Rates and Rates and

Zone Zone Broadening Broadening

on Resolution on Resolution

Migration Rates of SolutesMigration Rates of SolutesDistribution ConstantsDistribution Constants

• Migration rates are dependent on the magnitude of of the Migration rates are dependent on the magnitude of of the equilibrium equilibrium constantsconstants for the reactions by which the for the reactions by which the solutes distribute themselves solutes distribute themselves between the mobile and stationary phasebetween the mobile and stationary phase..

K = cK = css / c / cm m

where cwhere css = molar concentration of the solute in the = molar concentration of the solute in the stationary phasestationary phase

and cand cmm = molar concentration of the solute in the = molar concentration of the solute in the mobile phasemobile phase

• K is often referred to as the K is often referred to as the distribution coefficientdistribution coefficient, , partition coefficientpartition coefficient, , or or partition ratiopartition ratio

Migration Rates of SolutesMigration Rates of SolutesRetention TimesRetention Times

• The time it takes after sample injection for an analyte peak to The time it takes after sample injection for an analyte peak to reach the detector is called reach the detector is called retention timeretention time..

ttRR = L / v = L / vavgavg

Dead timeDead time

Where Where L = length of L = length of columncolumn vvavgavg = average = average

velocity of analytevelocity of analyte

Migration Rates of SolutesMigration Rates of SolutesVelocity of Mobile Phase Velocity of Mobile Phase

• Velocity of mobile phase can be calculated using tVelocity of mobile phase can be calculated using tMM. .

u = L / tu = L / tMM

Dead timeDead time

Where Where L = length of L = length of columncolumn uu = average = average velocity of an velocity of an unretained speciesunretained species

Migration Rates of SolutesMigration Rates of SolutesThe Relationship Between Retention Time and The Relationship Between Retention Time and

Distribution ConstantDistribution Constant • In order to relate the retention time of the solute to its In order to relate the retention time of the solute to its

distribution constant, we express its migration as a fraction of the distribution constant, we express its migration as a fraction of the velocity of the mobile phase.velocity of the mobile phase.

VVavgavg = u = u xx fraction of time solute spends in mobile phase fraction of time solute spends in mobile phase

** = capacity factor or retention factor

Migration Rates of SolutesMigration Rates of SolutesRelative Migration Rates: Relative Migration Rates: Selectivity FactorSelectivity Factor

• A fraction consisting of of the partition ratios of two retained A fraction consisting of of the partition ratios of two retained species on a chromatographic column; by convention the ratio of species on a chromatographic column; by convention the ratio of the more strongly held species the more strongly held species (K(Kbb,the species that takes longer to ,the species that takes longer to

elute)elute) is in the numerator. is in the numerator. By this definition By this definition is always greater is always greater than 1.than 1.

= K= KBB/K/KAA

= k’= k’BB / k’ / k’AA

= [(t= [(tRR))BB - t - tMM ] / [(t ] / [(tRR))AA – t – tMM]]

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyThe Shapes of Chromatographic PeaksThe Shapes of Chromatographic Peaks

• Gaussian curvesGaussian curves

• Random walkRandom walk

• The breadth of a band increases as it moves down the column The breadth of a band increases as it moves down the column because more time is allowed for spreading to occur. because more time is allowed for spreading to occur.

• The zone breadth (The zone breadth (peak widthpeak width) is directly related to residence time ) is directly related to residence time and inversely related to the velocity of the mobile phaseand inversely related to the velocity of the mobile phase

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyMethods for Describing EfficiencyMethods for Describing Efficiency

• The theory is based on work by Martin and Synge in which they treated a The theory is based on work by Martin and Synge in which they treated a chromatographic column as if it were a distillation columnchromatographic column as if it were a distillation column

= L/N= L/N

theoretical plate heighttheoretical plate height

N= number of theoretical platesN= number of theoretical plates

L= length of columnL= length of column

The The plate theoryplate theory successfully accounts for the Gaussian shape and their rate of successfully accounts for the Gaussian shape and their rate of movement down a column, but fails to account for peak broadening in a movement down a column, but fails to account for peak broadening in a mechanistic way. The mechanistic way. The rate theoryrate theory was developed to make up for these shortcomings. was developed to make up for these shortcomings.

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyMethods for Describing EfficiencyMethods for Describing Efficiency

• The theory is based on work by Martin and Synge in which they treated The theory is based on work by Martin and Synge in which they treated a chromatographic column as if it were a distillation columna chromatographic column as if it were a distillation column

= L/N= L/N

H = (LWH = (LW22)/(16t)/(16tRR22))

N = 16 (tN = 16 (tRR/W)/W)22

N = 5.54(tN = 5.54(tRR/W/W1/21/2))22

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyKinetic Variables Affecting Zone BroadeningKinetic Variables Affecting Zone Broadening

Zone Broadening Zone Broadening and Column and Column EfficiencyEfficiency

Kinetic Variables Kinetic Variables Affecting Zone Affecting Zone

BroadeningBroadening

Mobile-Phase Flow RateMobile-Phase Flow Rate

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyRelationship Between Plate Height and Column Relationship Between Plate Height and Column

Variables - Variables - van Deemter Equationvan Deemter Equation H = A + B/H = A + B/uu + C + Cuu H = A + B/H = A + B/uu +(C +(Css + C + Cmm))uu

Zone Broadening and Column EfficiencyZone Broadening and Column Efficiencyvan Deemter Equation - van Deemter Equation - The Multipath Term (A)The Multipath Term (A)

H =H = AA + B/ + B/uu + C + Cuu

A = 2A = 2ddpp

depends on particle size distribution, the depends on particle size distribution, the narrower the distribution the smaller the narrower the distribution the smaller the

The smaller the particle size, the smaller the The smaller the particle size, the smaller the A termA term

Independent of mobile phase flow rateIndependent of mobile phase flow rate

Also known as eddy diffusionAlso known as eddy diffusion

Zone Broadening and Column EfficiencyZone Broadening and Column Efficiencyvan Deemter Equation - van Deemter Equation - Longitudinal Diffusion (B)Longitudinal Diffusion (B)

H =H = A + A + B/B/uu + C + Cuu

B/u = 2B/u = 2DDMM/u/u

is related to the is related to the diffusion restrictiondiffusion restriction of of packed columns, with packed columns packed columns, with packed columns this value is about 0.6 and 1 for open this value is about 0.6 and 1 for open tubular columns tubular columns

DDMM is the mobile phase diffusion coefficient is the mobile phase diffusion coefficient

Inversely related to mobile Inversely related to mobile

phase flow ratephase flow rate

Negative slope due Negative slope due to this termto this term

less for LCless for LC

Zone Broadening and Column EfficiencyZone Broadening and Column Efficiencyvan Deemter Equation - van Deemter Equation - Mass Transfer (C)Mass Transfer (C)

H = A + B/H = A + B/uu + +(C(Css + C + Cmm))uu

CCSS = f = fSS(k’)d(k’)dff22

/ D/ DSS

CCMM = f = fMM(k’)d(k’)dpp22

/ D/ DMM

f(x) is a function of x f(x) is a function of x

DDMM is the mobile phase diffusion coefficient is the mobile phase diffusion coefficient

DDSS is the stationary phase diffusion coefficient is the stationary phase diffusion coefficient

ddff is film thickness is film thickness

ddpp is particle size is particle size

Directly related to mobile phase flow rateDirectly related to mobile phase flow rate

Zone Broadening and Column EfficiencyZone Broadening and Column Efficiencyvan Deemter Equation - van Deemter Equation - SummarySummary

H = A + B/H = A + B/uu + +(C(Css + C + Cmm))uu

Zone Broadening and Column EfficiencyZone Broadening and Column EfficiencyEffect of Particle Size on Plate HeightEffect of Particle Size on Plate Height

Optimization of Column PerformanceOptimization of Column Performance

• A chromatographic separation is optimized varying A chromatographic separation is optimized varying experimental conditions until the components of the experimental conditions until the components of the mixture are mixture are separated cleanlyseparated cleanly with a with a minimum minimum expenditure of timeexpenditure of time..

• Optimization experiments are aimed at Optimization experiments are aimed at – reducing zone broadeningreducing zone broadening

– altering relative migration rates of componentsaltering relative migration rates of components

Optimization of Column PerformanceOptimization of Column PerformanceColumn ResolutionColumn Resolution

• Resolution Resolution (R(RSS)) of a column provides a quantitative of a column provides a quantitative

measure of its ability to separate two analytesmeasure of its ability to separate two analytes

Effect of Retention and Selectivity Factors Effect of Retention and Selectivity Factors on Resolutionon Resolution

Column ResolutionColumn Resolution

• Resolution in terms of Resolution in terms of retention timesretention times and and efficiencyefficiency

• Resolution in terms of Resolution in terms of capacity factorscapacity factors and and efficiencyefficiency

Effect of Retention and Selectivity Factors Effect of Retention and Selectivity Factors on Resolutionon Resolution

Column ResolutionColumn Resolution

• Resolution in terms of Resolution in terms of capacity factorscapacity factors, , efficiency, efficiency, andand selectivity factorsselectivity factors

• EfficiencyEfficiency in terms of in terms of capacity factorscapacity factors, , resolution, resolution, andand selectivity factorsselectivity factors

Variables That Affect Column PerformanceVariables That Affect Column Performance

• Resolution in terms of Resolution in terms of capacity factorscapacity factors, , efficiency, efficiency, andand selectivity factorselectivity factor

First termFirst term related to the related to the kineticskinetics that lead to band broadening that lead to band broadening

Second term is a selectivity Second term is a selectivity term that is only related to term that is only related to the properties of the two the properties of the two solutessolutes

Third term depends on properties of Third term depends on properties of both the solute and the columnboth the solute and the column

Variation In Retention FactorVariation In Retention Factor

Variation In Retention FactorVariation In Retention Factor

General Elution ProblemGeneral Elution Problem

Important Chromatographic TermsImportant Chromatographic Terms

Important Chromatographic TermsImportant Chromatographic Terms