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Chem. 230 – 9/25 Lecture. Announcements I. Quiz 1 Results Solutions have been posted See class distribution Grade cut-offs have not been set, will depend somewhat on class scores Based on Quiz 1, I might expect cut-offs a couple of % below 90/80/70%. Announcements II.

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announcements i
Announcements I
  • Quiz 1 Results
    • Solutions have been posted
    • See class distribution
    • Grade cut-offs have not been set, will depend somewhat on class scores
    • Based on Quiz 1, I might expect cut-offs a couple of % below 90/80/70%
announcements ii
Announcements II
  • HW 2 long problems due next week
  • One group still needs to choose a topic for student presentations
  • What we are covering today?
    • More Definitions: Last question
    • Band broadening theory (Section 3.2)
    • Intermolecular Forces (Section 4.1)
    • Optimization (if time)
chromatographic theory questions on definitions
Chromatographic TheoryQuestions on Definitions
  • Given the two chromatograms to the right:
    • Which column shows a larger N value?
    • Which shows better resolution (1st 2 peaks top chromatogram)?
    • Which shows better selectivity (larger α; 1st 2 peaks on top)?
    • Should be able to calculate k, N, RS, and α

Unretained pk

chromatographic theory rate theory
Chromatographic TheoryRate Theory
  • We have covered parameters measuring column efficiency, but not covered yet what factors influence efficiency
  • In order to improve column efficiency, we must understand what causes band broadening (or dispersion)
  • van Deemter Equation (simpler form)

where H = Plate Height

u = linear velocity

and A, B, and C are “constants”

chromatographic theory rate theory1
Chromatographic TheoryRate Theory

Most efficient velocity


C term

B term

A term


chromatographic theory rate theory2
Chromatographic TheoryRate Theory

Inside of column

(one quarter shown)

  • How is u determined?
    • u = L/tM
    • u = F/A* (A* = effective cross-sectional area)
  • “Constant” Terms
    • A term: This is due to eddy diffusion
    • Eddy diffusion results from multiple paths

Shaded area = cross-sectional area = area*porosity





chromatographic theory rate theory3
Chromatographic TheoryRate Theory
  • A Term
    • Independent of u
    • Smaller A term for: a) small particles, b) spherical particles, or c) no particles (near zero)
    • Small particles (trend in HPLC) results in greater pressure drop and lower flow rates
chromatographic theory rate theory4
Chromatographic TheoryRate Theory
  • B Term – Molecular Diffusion
    • Molecular diffusion is caused by random motions of molecules
    • Larger for smaller molecules
    • Much larger for gases
    • Dispersion increases with time spent in mobile phase
    • Slower flow means more time in mobile phase




Band broadening

chromatographic theory rate theory5
Chromatographic TheoryRate Theory
  • C term – Mass transfer to and within the stationary phase
    • Analyte molecules in stationary phase are not moving and get left behind
    • The greater u, the more dispersion occurs
    • Less dispersion for smaller particles and thinner films of stationary phase
    • Less dispersion for solute capable of faster diffusion (smaller molecules)




Column particle

chromatographic theory rate theory6
Chromatographic TheoryRate Theory
  • More generalities
    • Often run at u values greater than minimum H (saves on time; reduces σ which can increase sensitivity depending on detector)
    • For open tubular GC, A term is minimal, C term minimized by using smaller column diameters and stationary phase films
    • For packed columns, A and C terms are minimized by using small particle sizes

Low flow conditions

Higher flow conditions

chromatographic theory rate theory7
Chromatographic TheoryRate Theory

Some Questions:

  • What are advantages and disadvantages of running chromatographs at high flow rates?
  • Why is GC usually operated closer to the minimum H value than HPLC?
  • Which term is nearly negligible in open tubular GC?
  • How can H be decreased in HPLC? In open tubular GC?
chromatographic theory effects of intermolecular forces
Chromatographic TheoryEffects of Intermolecular Forces
  • Phases in which intermolecular forces are important: solid surfaces, liquids, liquid-like layers, supercritical fluids (weaker)
  • In ideal gases, there are no intermolecular forces (mostly valid in GC)
  • Intermolecular forces affect:
    • Adsorption (partitioning to surface)
    • Phase partitioning
    • Non-Gausian Peak Shapes
chromatographic theory intermolecular forces asymmetric peaks
Chromatographic TheoryIntermolecular Forces – Asymmetric Peaks
  • More than one possible cause (e.g. extra-column dispersion)
  • One common cause is sample or analyte overloading of column
  • Analyte loading shown →
  • More common with solid stationary phase
  • More common with open tubular GC; less common with HPLC

5% by mass ea.

20% by mass ea.

chromatographic theory intermolecular forces asymmetric peaks1
Chromatographic TheoryIntermolecular Forces – Asymmetric Peaks

Low Concentrations

  • Most common for solid stationary phase and GC because
    • Less stationary phase (vs. liquid)
    • GC behavior somewhat like distillations
  • At low concentrations, column “sites” mostly not occupied by analyte
  • As conc. increase, % sites occupied by analyte increases, causing change in analyte – stationary phase interaction

Active sites



High Concentrations

New analyte






chromatographic theory intermolecular forces asymmetric peaks2
Chromatographic TheoryIntermolecular Forces – Asymmetric Peaks
  • As concentration increase, interactions go from analyte – active site to analyte – analyte
  • If interaction is Langmuir type (weak analyte – analyte vs. strong analyte – active site), tailing occurs (blocking of active sites causes additional analyte to elute early)
  • If interaction is anti-Langmuir type (stronger analyte – analyte interactions), fronting occurs (additional analyte sticks longer)

Tailing peak (up fast, down slow)

Fronting peak (up slow, down fast)

chromatographic theory intermolecular forces asymmetric peaks3
Chromatographic TheoryIntermolecular Forces – Asymmetric Peaks
  • If tailing is caused by saturation of stationary phase, changing amount of analyte injected will change amount of tailing and retention times
chromatographic theory intermolecular forces odd peak shapes
Chromatographic TheoryIntermolecular Forces – Odd Peak Shapes

Other Reasons for Odd Peak Shapes

  • Large volume injections
    • Example: 1.0 mL/min. + 0.1 mL injection

Injection plug time = 0.1 min = 6 s (so no peaks narrower than 6 s unless on-column trapping is used)

  • Injections at high temp./in strong solvents

Will not partition to stationary phase until mobile phase mixes in

In strong solvent




Analytes stick on column until stronger mobile phase arives



In weak solvent


chromatographic theory intermolecular forces odd peak shapes1
Chromatographic TheoryIntermolecular Forces – Odd Peak Shapes
  • Analyte exists in multiple forms
    • Example: maltotetraose (glu[1→4]glu[1→4]glu)
    • Has 3 forms (α, β, or aldehyde on right glu)
    • α and β forms migrate at different rates
    • At low T, interconversion is slow relative to tR. At high T, interconversion is faster
  • Extra-column broadening/turbulent flow
  • Multiple types of stationary phase

Low T

High T



Polar groups



Non-polar groups

chromatographic theory intermolecular forces types of interactions
Chromatographic TheoryIntermolecular Forces – Types of Interactions

Interactions by decreasing strength

Ion – Ion Interactions

Strong attractive force between oppositely charged ions

Of importance for ion exchange chromatography (ionic solute and stationary phase)

Also important in ion-pairing used in reversed-phase HPLC

Very strong forces (cause extremely large K values in absence of competitors)

From a practical standpoint, can not remove solute ions from stationary phase except by ion replacement (ion-exchange)

Ion – Dipole Interactions

Attractive force between ion and partial charge of dipole

d- d+



chromatographic theory intermolecular forces types of interactions1
Chromatographic TheoryIntermolecular Forces – Types of Interactions

Interactions by decreasing strength – cont.

Ion – Dipole Interactions – cont.

Determines strength of ionic solute – solvent interactions, ionic solute – polar stationary phase interactions, and polar solute – ionic stationary phase interactions

Important for some specific columns (e.g. ligand exchange for sugars or Ag+ for alkenes)

Metal – Ligand Interactions

ion – ion or ion – dipole interaction, but also involve d orbitals

chromatographic theory intermolecular forces types of interactions2
Chromatographic TheoryIntermolecular Forces – Types of Interactions

Interactions by decreasing strength – continued (non-ionic interactions = van der Waal interactions)

Van der Waals Forces

dipole – dipole interactions (requires two molecules with dipole moments)

important for solute – solvent (especially reversed phase HPLC) and solute – stationary phase (especially normal phase HPLC)

Hydrogen bonding is a particularly strong dipole-dipole type of bonding

dipole – induced dipole interactions

induced dipoles occur in molecules with no net dipole moment

larger, more electron rich molecules can get induced dipoles more readily

induced dipole – induced dipole interactions (London Forces)

occur in the complete absence of dipole moments

also occur in all molecules, but of less importance for polar molecules

chromatographic theory intermolecular forces types of interactions3
Chromatographic TheoryIntermolecular Forces – Types of Interactions

Modeling interactions

Somewhat of a one-dimensional model can be made by assigning a single value related to polarity for analytes, stationary phases, and mobile phases (See section 4.3)

These models neglect some interactions however (e.g. effects of whether an analyte can hydrogen bond with a solvent)

chromatographic theory intermolecular forces some questions
Chromatographic TheoryIntermolecular Forces – Some Questions

Describe the dominant forces involving the molecules to the right in interacting with non-polar molecules? in interacting with polar molecules

How does going from DB-1 (100% methyl stationary phase) to DB-17 (50% methyl – 50% phenyl) in GC affect elution of fatty acid methyl esters? (e.g. C16 vs. C18 vs. C18:1)

chromatographic theory intermolecular forces some questions1
Chromatographic TheoryIntermolecular Forces – Some Questions

Silica has many SiOH groups on the surface (pKa ~2). What interactions will occur with the analyte phenol, C6H5OH, if the eluent is a mixture of hexane and 2-propanol?

Sugars are often separated on amino columns. A sugar that has a carboxylic acid group in place of an OH group will have extremely large retention times (at least at neutral pH values). What does this say about the state of the amino groups?

chromatographic theory intermolecular forces some questions2
Chromatographic TheoryIntermolecular Forces – Some Questions

In reversed phase HPLC with a C18 column, benzene and methoxybenzene (anisole) have very similar retention times. What are the differences in the interactions between the two solutes and mobile phases and stationary phases?

A heavily used non-polar GC column is used to separate non-polar to polar columns. Polar compounds are observed to tail. A new column replaces the old column, tailing stops, and the polar compounds elute sooner. Explain the observations.

chromatographic theory optimization overview
Chromatographic TheoryOptimization - Overview

How does “method development” work?

Goal of method development is to select and improve a chromatographic method to meet the purposes of the application

Specific samples and analytes will dictate many of the requirements (e.g. how many analytes are being analyzed for and in what concentration?, what other compounds will be present?)

Coarse method selection (e.g. GC vs HPLC and selection of column type and detectors) is often based on past work or can be based on initial assessment showing problems (e.g. 20 compounds all with k between 0.2 and 2.0 with no easy way to increase k)

Optimization then involves making equipment work as well as possible (or limiting equipment changes)

chromatographic theory optimization some trade offs
Chromatographic TheoryOptimization – Some trade offs

Flow rate at minimum H vs. higher flow rates (covered with van Deemter Equation) – low flow rate not always desired because of time required and sometimes smaller S/N

Maximum flow rate often based on column/instrument damage – this can set flow rate

Trade-offs in reducing H

In packed columns, going to small particle sizes results in greater back-pressure (harder to keep high flow)

In GC, small column and film diameters means less capacity and can require longer analysis times

Trade-offs in lengthening column (N = L/H)

Longer times due to more column (often not proportional since backpressure at same flow rate will be higher)

chromatographic theory optimization improved resolution through increased column length
Chromatographic TheoryOptimization – Improved Resolution Through Increased Column Length


Compounds X and Y are separated on a 100 mm column. tM = 2 min, tX = 8 min, tY = 9 min, wX = 1 min, wY = 1.13 min, so RS = 0.94. Also, N = 1024 and H = 100 mm/1024 = 0.097 mm

Let’s increase L to 200 mm. Now, all times are doubled:

tM = 4 min, tX = 16 min, tY = 18 min. So DtR (or d) now = 2 min. Before considering widths, we must realize that N = L/H (where H is a constant for given packing material).

N200 mm = 2*N100 mm. Now, N = 16(tR/w)2 so w = (16tR2/N)0.5

w200 mm/w100 mm = (tR200 mm/tR100 mm)*(N100 mm/N200 mm)0.5

w200 mm/w100 mm = (2)*(0.5)0.5 = 21-0.5 = (2)0.5

w200 mm = 1.41w100 mm

RS = 2/1.5 = 1.33

Or RS 200/RS 100 = d/wave = (d200/d100)*(w100/w200)= (L200/L100)*(L100/L200)0.5

So RS is proportional to (L)0.5

chromatographic theory optimization resolution equation
Chromatographic TheoryOptimization – Resolution Equation

Increasing column length is usually the least desired way to improve resolution (because required time increases and signal to noise ratio decreases)

Alternatively, k values can be increased (use lower T in GC or weaker solvents in HPLC); or αvalues can be increased (use different solvents in HPLC or column with better selectivity) but effect on RS is more complicated

Note: above equation is best used when deciding how to improve RS, not for calculating RS from chromatograms