Introduction to Chromatography Theory

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Introduction to Chromatography Theory

• Bioanalytical Chemistry
• Spring 2004

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The Theory of Chromatography

• Plate theory - older developed by Martin Synge
  
• Rate theory - currently in use today

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Plate Theory - Martin Synge 1954 Nobel Laureates

• View column as divided into a number (N) of
  adjacent imaginary segments called theoretical
  plates
• within each theoretical plate complete
  equilibration of analytes between stationary and
  mobile phase occurs

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Plate Theory - Martin Synge 1954 Nobel Laureates

• Significance?Greater separation occurs with
• greater number of theoretical plates (N)
• as plate height (H or HETP) becomes smaller
• L N H or H L / Nwhere L is length of
  column, N is number of plates, and H is height of
  plates

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N can be Estimated Experimentally from a
Chromatogram

• N 5.55 tr2 / w1/22 16 tr2 / w2wheretr is
  retention timew1/2 is full width at maximumw
  is width measured at baseline

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Choice of Column Dimensions

• Nmax 0.4 L/dpwhereN - maximum column
  efficiencyL - column lengthdp - particle size
• So, the smaller the particle size the higher the
  efficiency!

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Efficiency Relative to Analysis Time
today90 mm L 3 um
today150 mm L 5 um
N
1970s300 mm L 10 um
Analysis Time, min
10
100
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First Important Prediction of Plate Theory

• Bandspreading - the width of bands increases as
  their retention time (volume) increases

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Problem

• A band exhibiting a width of 4 mL and a retention
  volume of 49 mL is eluted from a column. What
  width is expected for a band with a retention
  volume of 127 mL eluting from the same analyte
  mixture on the same column?
• ANS 10.4 mL

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Second significant prediction of plate theory

• The smaller HETP, the narrower the eluted peak

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Plate Theory - Practical Considerations

• Not unusual for a chromatography column to have
  millions of theoretical plates
• Columns often behave as if they have different
  numbers of plates for different solutes present
  in same mixture

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Rate Theory

• Based on a random walk mechanism for the
  migration of molecules through a column
• takes into account
• band broadening
• effect of rate of elution on band shape
• availability of different paths for different
  solute molecules to follow
• diffusion of solute along length

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Van Deemter Equation

• H A n1/3 B/n C nwhereH is HETP
  (remember want a minimum!)n is mobile phase
  velocityA, B, and C are constants

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Van Deemter Equation

• H A n1/3 B/n C n
• first term - rate of mobile phase movement
  through column (often just a constant)
• second term - longitudinal solute diffusion
  solute concentration always lower at edges of
  column so solute diffuses longitudinally
• third term - equilibration is not instantaneous

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Resolution

• Ideal chromatogram exhibits a distinct separate
  peak for each solute
• reality chromatographic peaks often overlap
• we call the degree of separation of two peaks
• resolution peak separation
  average peak width

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Resolution

• Resolution D tr / wavg
• lets take a closer look at the significance of
  the problem

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Resolution

• So, separation of mixtures depends on
• width of solute peaks (want narrow)efficiency
• spacing between peaks (want large
  spacing)selectivity

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Example

• What is the resolution of two Gaussian peaks of
  identical width (3.27 s) and height eluting at
  67.3 s and 74.9 s, respectively?
• ANS Resolution 2.32