Chromatography Zone Broadening and Resolution

History of Chromatography

• Russian botanist Mikhail Tswett coined the term "chromatography" in 1906 to describe his experiments in separating different colored constituents of leaves.

Principles of Chromatography

• Chromatography is a separation technique based on the different interactions of compounds with two phases: a mobile phase and a stationary phase.
• Components of Chromatography: mobile phase, stationary phase, and supporting medium.
• Chromatography separates components based on their interactions with the stationary and mobile phases.

Types of Chromatography

• Gas Chromatography (GC): uses a gas as the mobile phase.
• Liquid Chromatography (LC): uses a liquid as the mobile phase.
• Supercritical Fluid Chromatography (SCFC): uses a supercritical fluid as the mobile phase.
• Classification of Chromatography based on stationary phase:
  • Gas-Solid Chromatography: uses a solid stationary phase.
  • Gas-Liquid Chromatography: uses a liquid-coated stationary phase.
  • Bonded-Phase Gas Chromatography: uses a chemically-derivatized stationary phase.
• Classification of Chromatography based on attractive forces:
  • Adsorption Chromatography: for polar non-ionic compounds.
  • Ion Exchange Chromatography: for ionic compounds.
  • Partition Chromatography: based on the relative solubility of analyte in mobile and stationary phases.
  • Size Exclusion Chromatography: based on the size of the analyte.

Column Chromatography

• Packed Column: uses tiny particles as the stationary phase.
• Capillary Column: uses a small diameter tube coated with the stationary phase on the inside.

Planar Chromatography

• Thin-Layer Chromatography (TLC): uses a flat, uniform layer of stationary phase on a support.

Detectors

• UV-Vis Detector: detects absorbance of light by the analyte.
• Refractive Index (RI) Detector: detects changes in the refractive index of the mobile phase.
• Mass Spectrometry (MS) Detector: detects the mass-to-charge ratio of ions.
• Electrochemical (EC) Detector: detects the electrical signal generated by the analyte.
• NMR Detector: detects the nuclear magnetic resonance signal of the analyte.

Theory of Chromatography

• Chromatogram: a graphical representation of the detector signal vs. retention time or volume.
• Retention Time (tR): the time taken for an analyte to elute from the column.
• Void Time (tM): the time taken for a non-retained component to elute from the column.
• Capacity Factor (k'): a measure of the retention of an analyte, calculated as k' = (tR - tM)/tM.
• Efficiency (N): the number of theoretical plates in a column, calculated as N = (tR/σ)².
• Plate Height (H): the length of column required for one theoretical plate, calculated as H = L/N.
• Van Deemter Equation: a mathematical equation that relates the plate height to the linear velocity of the mobile phase.

Physicochemical Principles of Chromatographic Separation

• Adsorption Chromatography: separates based on Van der Waals forces, electrostatic forces, hydrogen bonds, and hydrophobic interactions.
• Partition Chromatography: separates based on differences in solubility in mobile and stationary phases.
• Ion-Exchange Chromatography: separates based on differences in affinity of ions for the exchangers.
• Size Exclusion Chromatography: separates based on the size of the analyte.
• Affinity Chromatography: separates based on bioselective interactions between the analyte and the ligand.### Chromatography Theory
• Partition Coefficient (K): ratio of the concentration of a solute in the organic phase to its concentration in the aqueous phase, represented by the equation K = Co/Cw, where Co is the concentration in the organic phase and Cw is the concentration in the aqueous phase.

Column Chromatography

• Dilution and Peak Broadening: occur when the mobile phase moves too quickly, causing the analyte molecules to spread out and overlap, resulting in poor resolution.

Distribution Constant (K) and Retention Times

• K: a measure of how much a solute is retained in the stationary phase, affecting its retention time.
• Retention Time (tR): the time it takes for an analyte to pass through the column, influenced by the distribution constant (K) and the mobile phase velocity.

Velocities and Retention Times

• Linear Rate of Solute Migration: the velocity of a solute is affected by the mobile phase velocity and the fraction of time spent in the mobile phase.
• Velocity of Solute: influenced by the distribution constant (K) and the mobile phase velocity, represented by the equation v = μ × (1 + KVS/VM).

Selectivity Factor (α)

• α: a measure of how well two analytes are separated, influenced by their respective distribution constants (K) and retention times, represented by the equation α = kB/kA.

Column Efficiency - Theoretical Plates

• Theoretical Plates (N): a measure of column efficiency, influenced by the plate height (H) and column length (L), represented by the equation N = L/H.
• Plate Height (H): a measure of the zone broadening, influenced by the mobile phase velocity (μ) and the plate height, represented by the van Deemter equation.

Zone Broadening

• Zone Broadening: the spreading of the analyte zone as it moves through the column, influenced by the mobile phase velocity (μ) and kinetic processes.
• Kinetic Processes: include multiple pathways, eddy diffusion, and longitudinal diffusion, which affect zone broadening.

Resolution

• Resolution (Rs): a measure of the separation between two peaks, influenced by the retention times, peak widths, and column efficiency, represented by the equation Rs = 2(tR,B - tR,A)/(wB + wA).

Gas Chromatography

• Injector: where the sample is introduced into the column.
• Detector: where the separated compounds are detected.
• Column Oven: where the column is heated to control the separation process.
• Carrier Gas: the mobile phase in gas chromatography, which must be inert to prevent interference with the separation process.

Advantages and Disadvantages of Gas Chromatography

• Advantages: only requires a small sample size, can analyze any compound that can be vaporized, is a fast and inexpensive method.

• Disadvantage: is a destructive technique, meaning the sample is lost after analysis.### Gas Chromatography

• Too hot temperatures can cause all compounds to vaporize and be carried rapidly through the column, resulting in no partitioning effect and thin, narrow peaks.

• Too cool temperatures can cause compounds to condense more than they should, resulting in broad and overlapped peaks.

Types of Analysis

• Qualitative Analysis: Identification of compounds using retention time (similar to Rf values for TLC).
• Retention time: The amount of time it takes for a compound to travel through the column, from the point of vaporization to the detector.
• Example: Compound X has a retention time of 3.1 minutes, Compound Y has a retention time of 4.8 minutes, and Compound Z has a retention time of 5.3 minutes.

Quantitative Analysis

• Determination of relative amounts of each compound (ratio of compounds).
• Step 1: Calculate the area under the peaks using the equation: Area = (height of peak) x (width at half the height).
• Step 2: Calculate the Percent Composition (Relative Amounts) by dividing each individual area by the sum total of all areas x 100.

Internal Standard

• A compound added to the sample in a known and constant concentration.
• Ratio of its retention time to the retention times of the target compounds and ratio of its peak area to the peak areas of target compounds are determined for various concentrations of the target compounds.
• Preferred technique because it corrects for errors in sample preparation and variations in the amount of sample injected.

External Standard

• Known amounts of analytes are run in separate analyses, and the resulting peak areas are used to obtain calibrated response factors.
• Concentrations of the analytes are calculated by applying the response factors obtained from the standard runs.

Quantitation in Chromatography

• Detector Response: Depends on the concentration of the analyte or mass of the analyte reaching the detector.
• Detector Noise: Present in all detectors, can be high or low frequency.
• Ability to detect small quantities depends on the signal (peak height) to noise ratio.

Levels of Detection and Quantitation

• Noise can have high and low frequency parts.
• Ways of defining noise: peak to peak (roughly 5σ) or standard deviation (more accurate way).

Data Smoothing

• Data should be digitized with a frequency ~20/peak width.
• High frequency noise can be removed by filtering, but over-filtering can result in reduction of signal and loss of resolution.

Integration

• Integration of peak should give peak height, peak area, and peak width.
• Difficulty comes from determining if a peak is a peak (or just noise) and when to start and end the peak.
• Can use auto integration or manual integration.

Integration Issues

• Other issues in integration: start and ends to peaks, how to split overlapping peaks.

Peak Height vs. Peak Area

• Reasons for using peak area: peak area is independent of retention time, peak area is independent of peak width.
• Reasons for using peak height: integration errors tend to be smaller if samples are close to the detection limits.

Calibration Methods

• External Standard: Most common method, standards run separately and calibration curve prepared.
• Internal Standard: Useful for GC with manual injection, standard added to sample, and calibration and sample determination based on peak area ratio.

Recovery Standards

• Principle of use is similar to standard addition, useful for determining losses during extractions, derivatization, and with matrix effects.

Additional Questions/Problems

• Questions and problems related to retention times, GC and TLC, and chromatograph analysis.

Chromatography Efficiency

• Higher α (selectivity) means larger differences in retention time and more separation between peaks.
• Efficiency (N) is a factor used to describe peak width, with high efficiency corresponding to narrow peaks.

Number of Theoretical Plates (N)

• N is calculated using the formula: N = L/H, where L is the column length and H is the plate height (both in the same units).
• N can be measured from peaks on a chromatogram using the formula: N = 5.54 (tr/W1/2)^2, where tr is the retention time and W1/2 is the peak width at half height.
• N is independent of solute retention and dependent on the length of the column.

Resolution (Rs)

• Resolution is the distance between two peaks and is a function of three factors: retention (k), selectivity (α), and efficiency (N).
• Rs can be calculated using the formula: Rs = ¼ (α-1/α) (k/k+1) N½.
• Increasing α, k, or N increases Rs.

Column Efficiency (N) and Plate Height (H)

• Plate height (H) relates to the length of the column that corresponds to one theoretical plate.
• H is dependent on kinetic variables such as flow rate and particle size.
• Rate theory of chromatography takes into account the time taken for solute equilibration between the stationary and mobile phase.

Selectivity Factor (α)

• α is a measure of how well two peaks can be separated.
• B retained more than A → α > 1.
• Selectivity factor can be calculated using the retention factors kA and kB.

Retention Time and Column Length

• Retention time (tR) is related to the column length (L) and standard deviation (σ): σ = L/tR.
• Column length is related to the standard deviation (σ) and plate height (H): H = L/N.

Theoretical Plates (Plate Model) and Rate Theory

• Plate model assumes infinitely fast equilibrium between mobile and stationary phases.
• Rate theory takes into account the time taken for solute equilibration between phases.
• Factors affecting peak broadening include eddy diffusion, mobile phase mass transfer, and stagnant mobile phase mass transfer.

Peak Width and Efficiency

• Peak width (Wb) is related to efficiency, with narrower peaks indicating higher efficiency.
• Peak width can be used to estimate standard deviation (σ) assuming a Gaussian-shaped peak.

Zone Broadening and Kinetic Processes

• Zone broadening is related to kinetic processes, including eddy diffusion, mobile phase mass transfer, stagnant mobile phase mass transfer, stationary phase mass transfer, and longitudinal diffusion.
• The Van Deemter Equation is H = A + B/μ + (CS + CM)μ, where H is the plate height, A is the multipath term, B is the coefficient of longitudinal diffusion, CS and CM are coefficients of mass transfer in the stationary and mobile phases, respectively, and μ is the linear velocity.

Eddy Diffusion

• Eddy diffusion is a band broadening process that results from different path lengths passed by solutes through a packed column.
• It is directly proportional to the diameter of the packing material.
• Eddy diffusion is offset by ordinary diffusion.
• Lower mobile-phase velocity leads to smaller eddy diffusion.

Mobile Phase Mass Transfer

• Mobile phase mass transfer is a process of peak broadening caused by the presence of different flow profiles within channels or between particles of the support in the column.
• It leads to band broadening due to differences in the rate of solute molecules moving through the column.

Stagnant Mobile Phase Mass Transfer

• Stagnant mobile phase mass transfer is a band broadening process due to differences in the rate of diffusion of solute molecules between the mobile phase outside the pores of the support and the mobile phase within the pores.
• The degree of band-broadening depends on the size, shape, and pore structure of the packing material, the diffusion and retention of the solute, and the flow rate of the solute through the column.

Stationary Phase Mass Transfer

• Stationary phase mass transfer is a band broadening process due to the movement of solute between the stagnant phase and the stationary phase.
• The degree of band-broadening depends on the retention and diffusion of the solute, the flow rate of the solute through the column, and the kinetics of interaction between the solute and the stationary phase.

Longitudinal Diffusion

• Longitudinal diffusion is a band broadening process due to the diffusion of the solute along the length of the column in the flowing mobile phase.
• The degree of band-broadening depends on the diffusion of the solute and the flow rate of the solute through the column.

Theory of Chromatography

• The rate theory of chromatography explains the kinetics of the chromatographic process.
• The theory of chromatography includes the Van Deemter Equation, eddy diffusion, mobile phase mass transfer, stagnant mobile phase mass transfer, stationary phase mass transfer, and longitudinal diffusion.

Column Efficiency

• Column efficiency is a measure of the number of theoretical plates in a column.
• The number of theoretical plates (N) is calculated using the equation N = 16(tR / W)², where tR is the retention time and W is the peak width.

Plate Theory

• Plate theory successfully accounts for peak shapes and rates of movement.
• However, it does not account for the mechanisms causing peak broadening, the effects of other parameters, or how to adjust experimental parameters.

Rate Theory

• Rate theory relates zone broadening to mass transfer processes.
• It explains the kinetics of the chromatographic process.

Column Efficiency and Flow Rate

• The flow rate of the mobile phase affects column efficiency.
• Liquid chromatography and gas chromatography have different flow rates and plate heights.

Mass Transfer Terms Cs and Cm

• Cs and Cm are coefficients of mass transfer in the stationary and mobile phases, respectively.
• Equilibrium between the mobile and stationary phases is never realized, leading to mass transfer effects on peak broadening.

Distribution Constant (K)

• The distribution constant (K) is the ratio of the concentration of the solute in the stationary phase to the concentration in the mobile phase.
• K is a constant in linear chromatography and affects retention times.
• Manipulating K can be done by adjusting the stationary phase, mobile phase, or temperature.

Retention Times

• Retention times are affected by the distribution constant (K).
• The retention time of the mobile phase (tM) is the dead time, while the retention time of the analyte (tR) is the time spent in the stationary phase.

This quiz covers the concepts of zone broadening, longitudinal diffusion, and resolution in chromatography, including the effects of μ and H on column performance.