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Analyze Complex mixtures
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If analyte produce overlapping signals
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Process of unmixing a sample
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Input energy
Analyte are diluted |
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Stationary Phase (SP)
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Fixed in column
Interacts with analyte |
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Mobile Phase (MP)
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Moves through/over SP
Carries analyte |
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Interactions
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No interaction with SP
Travel same speed as MP No retention = No separation |
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Interaction with SP
Analyte are retained Dispersion Part time in SP (v=0) and MP (same speed) |
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All analyte spends same amount of time in MP but diff. time in SP
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Retention
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Peaks located in chromatogram
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Analyte interaction with column
stationary phase: strongint. = slow rate |
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Control by thermodynamic property
alter property = alter retention Example: Temperature (GC) MP (LC) SP Analyte |
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Dispersion
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Band Broadening
peak width how dilute Ex: Dispersion = Intensity = [Analye] |
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Depends on structure of column
Analyte mix = Dispersion |
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Depends on diffusion of analyte
Diffusion Coefficient = Dispersion |
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Depends on total time in column
Time Diffusion = Dispersion |
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Occurs in tube/plate (TLC)
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Drive MP through column
consistent velocity Use a pump (LC) HPLC Use capillary action (TLC) Dip plate in MP Use gas pressure (GC) Store MP in HP-cylinder + attach to gas regulator |
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Introduce sample at top of column
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Allow MP to drive sample through/over SP
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Detector at end (emerges vs. time)
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Measure Retention (K')
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Variables
L=Length of column U= MP velocity V = Analyte velocity t m = retention time of MP t r=retention time of retained species K=distribution constant C s= [Analyte] in SP C m= [Analyte] in MP |
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t
r use to identify analyte |
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Simple matrix 1< K' <10
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Complex matrix 0.5< K' <20
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K'
Determined by chromatogram Controlled by equillibrium Judge separation by the last peak retention value |
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Control Retention
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Connect to K
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Control by thermodynamic property
Adjust temperature Adjust type of MP Adjust "strength" of MP/SP Add additives to MP interact with analyte, SP, MP Velocity of MP does not alter retention |
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Quantify Efficiency
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Treat chromatographic peaks like "Gaussian" peaks
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Mean = Retention time
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Quantify width peak
standard deviation peak width |
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Smaller width = better efficiency
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Narrow peaks = Good efficiency
Clear separation |
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Broad peaks = Poor efficiency
Overlapping |
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Peak Shapes
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Sample volume ~ 1% column volume
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Various processes in column spread into larger volume
Often significant > starting volume Ex: Inj.volume = 25uL and detection volume = 200uL |
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Desirable
Narrow peaks and small volume |
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"Gaussian Peaks"
Peak could emerge with neighbor peak dilution can form broadening |
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Measure Efficiency
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Variables
N = # of theoretical plate H = Height of theoretical plate (HETP) L= Lenght of column W = peak width at baseline σ = Standard deviation (unit of lenght) |
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Desirable
N = H = σ |
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W range = -2τ tp + 2τ
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N should be consistent
t r and σ scale with each other |
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If Baseline not Accessible
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Baseline peak width cannot be measured
nearby overlapping peaks |
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Use upper portion of peak that is undistorted
Use full-width at half maximum (FWHM) establish SD |
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W
1/2≠ 1/2 W |
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Occurrences
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Low efficiency
Not fully separated peaks Interferences |
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Dispersion is independent of retention
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Van Deemeter Overview
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A-Term
Associate with multiple flow paths through column Each unique distance Result in variety of times to transit column |
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B-Term
Associate with longitudinal diffusion of analyte Some analyte will arrive sooner/later Depends on magnitude + direction of net diffusion during t r |
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C-Term
Split into 2 sub-terms Relate to reality that chromatogram is carried out in non-equilibrium state Analyte in Mp will be out of equilibrium with those in SP (vice versa) Some analyte will arrive at detector earlier or later than true equilibrium would predicted |
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Van Deemeter Graph
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Produce the overall curve with distinct minimum
Corresponding to N max and fixed L |
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Overall Plate Height:
Equation: H = A + B/U + (C s+Cm)USum of 4 components (red line) |
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A-Term:
Constant (purple line) |
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B/U-Term:
Varies as 1/U (pink line) |
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C
sU-Term: Linear increasing (blue line) |
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C
mU-Term: Linear increasing (yellow line) |
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All molecules start at top of column
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As they move down
Follow different paths through particles Irrespective of interaction with SP |
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Range of paths depends on size of particles
Size = # of paths = Path length |
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Depends on how "packed: the bed is
Crack, voids, etc |
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Equation:
H A-term= 2λdpλ = quality/tortuosity factor ~0.5-0.6 (packed column) FSOT less |
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All molecules start at top of column
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As they move down
Molecules moves away from each other Process continues as long as they remain in column |
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Dispersion in all 3 directions
Only longitudinal dispersion impacts peak width ( and ) |
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Packing column
Reduce longitudinal diffusion = Plate height (Beneficial) Blocks molecules travel |
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Equation:
H B/U-Term = (2𝛾Dm)/U D m= Diffusion coefficient in MP 𝛾= Obstruction factor 0.6 (packed column) 1.0 ( open tubular column) U= MP velocity |
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C-Term
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Ideal chromatography
Assumption that analyte can "instantly" equilibrate between 2 phases |
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MP is always moving the analyte down
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Analyte in leading edge of peak are always moving over SP that is deficient in analyte
Reverse for trailing edge Out of equilibrium |
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Equilibrium established when there are analyte at:
SP MP Interface |
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Takes time for analyre to diffuse to/away from phases to match equilibrium constant
In SP Analyte gets further behind than expected In MP Analyte gets further ahead than expected |
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Rise to broadening
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C
mU-Term: Resistance to Mass Transfer in MP |
Space in-between particles depends on particles size/diameter
Distance required for diffusion to move analyte Reach interface |
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Delays in reaching equilibrium depends on distances
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Distance is proportional to size of particle
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Equation:
H CmU = (fm(K')dp2*U)/Dmf m(K') = Quasi constant Depends on retentiond p= Particle diameter (units) D m= Diffusion coefficient of analyte in MP (cm2/s) 1 cm2= 104mm U= MP velocity |
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C
sU-Term: Resistance to Mass Transfer in SP |
Space in SP depends on SP thickness
Distance required for diffusion |
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Analyte reach MP/SP interface
Equilibrium reach Delays depends on distances |
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Equation:
H CsU= (fs(K')df2*U)/Ds d f= SP thickness D s=Diffusion Coefficient of analyte in SP |
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GC:
~0.1-0.5 µm film thickness Controls retention Impact resistance to mass transfer |
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LC:
Never adjust to thickness Monolayer Resistance Negligible Important in MP |
mU and CsU Term Diagram
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Define Resolution
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2 peaks of interest (critical pair)
Peaks closest together |
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Resolved
Clear separation No analyte mixing Pure peaks |
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W is not affected by plate height
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Successful Separation
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Isolated peaks
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See baseline between peaks
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Dependent on resolution
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Can use ruler to see if baseline from beginning/end match to baseline between peaks
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Quantify Resolution (R/R
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Use W
Captures +/- 2𝜎 regions of "Gaussian" peaks Corresponds to ~ 95.5% of analyte |
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R improves:
Greater ∆t rSmaller W a and/or WbNarrow peaks = more baseline expose |
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Full W of peak does not matter
Only back half (peak 1) and first half (peak 2) |
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2 neighbouring peaks are resolved when R ≥1.5
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Control Resolution
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Proximity of 2 peaks is important to R
Controlled by separation conditions |
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Quantify proximity:
Selectivity factor Define as a ratio of distribution constant of 2 peaks |
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Peaks shares column Same SP and MP
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𝛼 = ratio of retention factors
Access from chromatogram Change in selectivity = change in resolution |
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Effects of Retention and Selectivity on R'
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Key variable that controls potential resolutions
Resolving power (R') |
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R' dependent:
Very sensitive to selectivity (𝛼) Somewhat sensitive to retention (K') Moderately sensitive to efficiency of column (N) Choice of column Choice of MP (LC only) |
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𝛼 control by:
Differential interactions between: Analyte MPSP |
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N control by:
Column (L) VD equations Type of column SP thickness Operating conditions |
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K' control by:
SP type Phase Ratio (SP thickness) MP type (LC only) |
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Effects of R' on Retention Time
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R'= Total run time
Interplay |
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Interplay between R' and t
r as a function of K' |
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R':
N and 𝛼 ~ constant when K' is alter Replace terms with Q |
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t
rb: N,H,𝛼, U ~ constant Assume R' is not changing dramatically Replace constant terms with Q |
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