Chromatography Kinetics: Band Broadening

• Chromatography is a separation technique to separate mixture components using their physical and chemical properties
• It uses a mobile phase to carry the mixture via stationary phase
• Separation occurs as differing components interact with the stationary phase differently

Chromatography Kinetics

• Kinetics in chromatography is about the rate at which solutes move through a chromatographic system
• Kinetics also focuses on the factors that affect the efficiency of the separation
• Key kinetic parameters:
  • Band broadening
  • Plate height
  • Resolution

Band Broadening

• Band broadening is the increase in width of a solute band when traveling through a chromatographic column
• Separation efficiency decreases because broader bands can overlap, thus making it harder to distinguish components

Band Broadening Factors

• Eddy diffusion:
  • Happens because of multiple path lengths through the stationary phase
  • Molecules take slightly different routes, causing band broadening
  • More significant in packed columns with irregular particle sizes
• Longitudinal diffusion:
  • Solutes diffuse in the mobile phase along the column's length
  • Significant band broadening occurs when more time is spent in the column
  • More significant with low flow rates
• Mass transfer:
  • Resistance to mass transfer is shown between the mobile and stationary phases
  • Solutes require movement between phases to separate
  • Slow mass transfer causes non-equilibrium conditions with band broadening

Plate Height (H)

• Plate height is a measurement of chromatographic column efficiency
• Plate height shows the column's length, which is needed for a theoretical separation step
• Lower plate height means higher column efficiency
• The Van Deemter equation mathematically shows the correlation between plate height to the linear velocity of the mobile phase:
  • H = A + B/u + Cu
    • H: Plate height
    • A: Eddy diffusion term
    • B: Longitudinal diffusion term
    • u: Linear velocity of the mobile phase
    • C: Mass transfer term
• A, B, and C are coefficients related to band broadening

Van Deemter Equation Terms

• Eddy diffusion (A):
  • This is independent of flow rate
  • Eddy diffusion depends on the particle size, and stationary phase packing
• Longitudinal diffusion (B/u):
  • Inversely proportional to the flow rate
  • Longitudinal diffusion becomes more significant at lower flow rates
• Mass transfer (Cu):
  • Proportional to flow rate
  • Depends on the diffusion coefficients inside the solute, in mobile and stationary phases, plus dimensions of the stationary phase

Resolution (Rs)

• Resolution is a quantitative measurement of separation between two peaks on a chromatogram
• This depends on the difference in retention times, and the peak widths
• Rs = (tR2 - tR1) / [(w1 + w2)/2]
  • Rs: Resolution
  • tR1, tR2: Retention times of the two peaks
  • w1, w2: Peak widths at the base
• Better separation exists at higher resolution

Resolution Factors

• Column efficiency (N):
  • Better resolution exists at higher efficiency (lower plate height)
  • This is increased by using smaller particle sizes plus optimizing column packing
• Selectivity (α):
  • This is the ratio of retention factors of the two solutes
  • α = k2/k1, where k is the retention factor
  • When there is a higher selectivity the resolution is better
  • Adjustments happen by changing the mobile phase composition, or stationary phase chemistry
• Retention factor (k):
  • The retention factor measures how much a solute is retained by the stationary phase
  • k = (tR - tM) / tM
    • tR: Retention time of the solute
    • tM: Retention time of an unretained compound
  • Optimizing k results in improved resolution

Chromatography Thermodynamics

• How solutes distribute in equilibrium between phases is what thermodynamics in chromatography looks at
• The equilibrium constant (K) is a key to describing the distribution

Equilibrium Constant (K)

• K = Cs / Cm
  • Cs: Solute concentration located in the stationary phase
  • Cm: Solute concentration housed in the mobile phase
• K describes how strong the affinity is of the solute for the stationary phase vs the mobile phase
• Greater K indicates a stronger interaction with the stationary phase

Relationship Between K and Gibbs Free Energy (ΔG)

• ΔG = - RT ln K
  • ΔG: Gibbs free energy change
  • R: Gas constant
  • T: Absolute temperature
  • K: Equilibrium constant
• ΔG can be shown via enthalpy (ΔH) and entropy (ΔS):
  • ΔG = ΔH - TΔS

Enthalpy (ΔH)

• ΔH is the heat absorbed or released when a solute transfers from the mobile to stationary phase
• Negative ΔH indicates an exothermic process, showing favorable binding when in the stationary phase
• Positive ΔH indicates an endothermic process, showing unfavorable binding when in the stationary phase

Entropy (ΔS)

• ΔS reflects how disorder changes when a solute transfers from the mobile to the stationary phase
• Negative ΔS indicates that disorder decreases, meaning the solute becomes more ordered when in the stationary phase
• Positive ΔS indicates the opposite, which would mean disorder increases and the solute becomes more disordered when in the stationary phase

Temperature Effects

• The equilibrium constant, retention, and separation are all impacted by temperature
• The temperature dependence of the equilibrium constant is described using the Van't Hoff equation:
  • ln K = -ΔH / (RT) + ΔS / R
• A linear plot, of ln K vs 1/T, shows a slope of -ΔH/R, plus an intercept of ΔS/R
• In gas chromatography:
  • Increasing temperature usually decreases retention times, because solutes spend less time in the stationary phase
• In liquid chromatography:
  • Temperature impacts are more complex, which rely on specific interactions between the solute, mobile phase, and stationary phase
  • Temperature can be used to adjust separation

Adsorption Isotherms

• Adsorption isotherms describe the relationship between the concentration of a solute adsorbed on the stationary phase, and the concentration in the mobile phase when at equilibrium
• Common isotherms:
  • Linear isotherm:
    • Cs = K Cm
    • Assumes that adsorption is directly proportional to concentration in the mobile phase, a simple model
  • Langmuir isotherm:
    • Cs = (Cs,max * K * Cm) / (1 + K * Cm)
    • Accounts for stationary phase saturation
    • Cs,max is the maximum concentration of solute that can be adsorbed
  • Freundlich isotherm:
    • Cs = K Cm^(1/n)
    • An empirical model accounting for heterogeneous adsorption sites
    • n is an empirical constant
• Peak shape is affected by the isotherm shape
  • Symmetrical peaks happen from Linear isotherms
  • Non-linear isotherms result in peak tailing or fronting

Applications

• The ability to optimize separation conditions comes via chromatography kinetics and thermodynamics
• Core principles for:
  • Selecting appropriate stationary and mobile phases
  • Optimizing flow rates and temperatures
  • Improving resolution and separation efficiency
  • Developing improved separation methods