Analytical Chemistry Chromatographic Separations KAM021 2016 Dr. A. Jesorka, 6112, aldo@chalmers.se
Introduction to Chromatographic Separations Theory of Separations -Chromatography Terms Summary: Chromatography Separation Principles Plate Theory vandeemter Equation Rate theory Variables Effecting Column Efficiency The General Elution Problem
Chromatographic Separation
Chromatography Chromatography is the separation of an analyte from a complicated mixture of similar constituents for qualitative or quantitative identification Applies to organic and inorganic as well as natural compounds
Basic Separation Principles and Terms Compounds (analytes) are separated from a mixture by passing them through a stationary phase using a mobile phase carrier Mobile phase = pure solvent or solvent mixture Stationary phase = column (packing) material
Basic Separation Principles and Terms Separations occur because analytes in the mobile phase interact with the stationary phase at different rates Produces varying migration rates for analytes Separation Interactions Partition Adsorption Ion Exchange Size Exclusion Affinity
Basic Separation Principles Example: Column elution chromatography Introduce two solutes (A & B) onto a packed column through which a mobil phase (i.e. solvent) or eluent is continuously pumped Chromatogram
Basic Separation Principles Separations depend on the extent to which solutes partition between the mobile and stationary phases We define this interaction as partition (distribution) coefficient: K = c s /c m Where: c s = stationary phase concentration (molar) c m = mobile phase concentration (molar)
Abundance The Chromatogram D E C A B Chromatograph The time that a peak appears (it s retention time) is specific for a given compound Sample Mixture Chromatogram A B C D E The relative size of a peak (area or height) is proportional to the relative abundance of the compound in the mixture 0 5 10 15 20 Time (minutes)
Chromatography Terms A number of terms can be defined from the following chromatogram: Dead time Retention time
Chromatography Terms Retention Time (t R ) = the time it takes after injection for a solute to reach the detector Dead time (t M ) = the time for an unretained species to reach the detector Mobile phase velocity (u) = L/t M The average linear rate of movement of molecules in the mobile phase Linear Rate of solute migration ( v ) = L /t R L = length of chromatographic column
Chromatography Terms Retention Factor or Capacity Factor k A term used to describe the migration rate of solutes (analytes) on columns Where: k ' ( A ) ( A) K (A) = is the distribution constant for species A V S = volume of stationary phase V M = volume of the mobile phase K V M V S
Chromatography Terms The capacity factor can be determined directly from a chromatogram using: k t ' R M t M t
Chromatography Terms Interpreting the retention factor: If k < 1; the elution is too rapid for accurate determination of t R. If k > approx. 10; the elution is too slow to be practical The preferred range for k is between 1 and 5
Chromatography Terms Selectivity Factor (a) = K B /K A Where K B is the distribution constant of the more strongly retained species (so that a >1) The selectivity factor can also be defined in terms of retention factors and retention times: a k ' t t k ' t t ( B) R( B) M ( A) R( A) M
Chromatography Terms Zone Broadening or Band Broadening Refers to the shape of a peak as a solute migrates through a chromatographic column; it will spread out and shorten in height with distance migrated
Longitudinal Diffusion
H = A + B/u + Cu Packed columns ABC <> 0 Open columns A = 0 CE (no stationary phase) AC = 0
Chromatography Terms Plate Height (H) and (number of) Theoretical Plates (N) Terms used to quantitatively describe chromatographic column efficiency Column efficiency increases as N increases where: N = L/H N = the number of interactions (i.e. transitions between mobile and stationary phases) that a solute has during its residence in the column H= the distance through the column a solute travels between interactions (typically given in centimeters)
Chromatography Terms Plate Theory used to describe solute migration through a column and the Gaussian shape of a peak If the shape of a chromatographic peak is assumed to be Gaussian, then the plate height can be defined in statistical terms involving standard deviation (σ) H L 2
Chromatography Terms Plate Theory (cont.) H is defined as variance per unit length of column H is the length of column that contains the fraction of analyte between L and L σ This is 34% of the analyte (1/2 σ)
Calculation of N from a Chromatogram Where: W = magnitude of the base of the triangle (in units of time) t M = retention time of an unretained solute t R = retention time of the solute N 16 t R W 2
Chromatography Terms Rate Theory (or Kinetic Theory) used to quantitatively explain the shapes of chromatographic peaks and the effects of chromatographic variables on peaks - as a solute migrates through a column The Gaussian shape of an peak can be attributed to the additive combination of the random motions of individual solute molecules The migration of an individual molecule through a column is irregular (based on random walk mechanism) The time an individual molecule spends in a phase depends upon (accidentally) gaining sufficient thermal energy to change phases Results in a symmetric spread of velocities around the mean
Chromatography Terms Column Resolution (R S ) is a quantitative measure of the ability of a column to separate two analytes: R S 2( t t ) R( B) R( A) W A W To increase resolution increase column length (L) B R S = 0.75 R S = 1 R S = 1.5 Limitation: longer time and broader bands Usually compromise between resolution and speed of analysis
Variables Effecting Separation Efficiency Particle Size of Packing (as size, N and H ) Immobilized Film Thickness (as film thickness, N and H ) -due to faster diffusion rates in film Viscosity of Mobile Phase (as viscosity, N and H ) Temperature (as T, k', but a remains approximately constant) Linear Velocity of Mobile Phase; u = L/t M (u is proportional to 1/t M because L = constant) Column Length (as L, N but H = constant, and separation efficiency ) In general, Separation (or Column) Efficiency, as N and H
Variables Effecting Column Mobile Phase Flow Rate Efficiency Optimum flow rate corresponds to minimum H Liquid Chromatography H is much smaller for HPLC than for GC (more efficient), but in practice GC columns are much longer than for HPLC Gas Chromatography Hence greater N for GC!
Variables Effecting Column Efficiency Particle Size of Column Packing The smaller the packing particles, the greater the column efficiency.
The General Elution Problem It is often difficult to find a set of conditions which will resolve all peaks to the same degree and also permit reliable quantification Solutions Multiple runs at different conditions Programmed elution (change conditions during the run)
Appendix
Summary of Important Terms 1 (Dead time)
Summary of Important Terms 2 Capacity Factor
EXAMPLE PROBLEM: Substances A and B were found to have retention times of 6.4 and 14.4 min, respectively, on a 22.6 cm column. An unretained sample of air passed through the column in 1.30 min. The widths of the peak bases were 0.45 and 1.07 min. Calculate the: (a.) column resolution (b.) the available no. of plates in the column (c.) the plate height (d.) the length of column required to achieve a resolution of 1.5 Read and study chapters on HPLC and GC
App. 1 - Column Chromatography Methods