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The basic theory of chromatography
Separation Theory
Analyze Complex mixtures |
If analyte produce overlapping signals |
Process of unmixing a sample |
Input energy
Analyte are diluted |
Requirements
Stationary Phase (SP) |
Fixed in column
Interacts with analyte |
Mobile Phase (MP) |
Moves through/over SP
Carries analyte |
Interactions |
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 |
Fundamental Processes
Retention |
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 |
Dispersion |
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 |
Separation Process
Occurs in tube/plate (TLC) |
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 |
Introduce sample at top of column |
Allow MP to drive sample through/over SP |
Detector at end (emerges vs. time) |
Retention
Measure Retention (K') |
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 |
Control Retention |
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 |
Efficiency
Quantify Efficiency |
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 |
Peak Shapes |
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 |
Measure Efficiency |
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 |
If Baseline not Accessible |
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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Full-Width at Half Maximum
Band Broadening
Occurrences |
Low efficiency
Not fully separated peaks
Interferences |
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Dispersion is independent of retention |
Van Deemeter Overview |
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 |
Van Deemeter Graph |
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
+C m
)U Sum 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 s
U-Term: Linear increasing (blue line) |
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C m
U-Term: Linear increasing (yellow line) |
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A-Term: Multipath Band Broadening
All molecules start at top of column |
As they move down
Follow different paths through particles
Irrespective of interaction with SP |
Range of paths depends on size of particles
Size = # of paths = Path length |
Depends on how "packed: the bed is
Crack, voids, etc |
Equation: H A-term
= 2λd p
λ = quality/tortuosity factor ~0.5-0.6 (packed column) FSOT less |
B/U-Term: Longitudinal Diffusion
All molecules start at top of column |
As they move down
Molecules moves away from each other
Process continues as long as they remain in column |
Dispersion in all 3 directions
Only longitudinal dispersion impacts peak width ( and ) |
Packing column
Reduce longitudinal diffusion = Plate height (Beneficial)
Blocks molecules travel |
Equation: H B/U-Term
= (2𝛾D m
)/U D m
= Diffusion coefficient in MP 𝛾= Obstruction factor ~ 0.6 (packed column) ~ 1.0 ( open tubular column) U= MP velocity |
C-Term: Resistance to Mass Transfer
C-Term |
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 |
Cm
U-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
= (f m
(K')d p
2*U)/D m
f m
(K') = Quasi constant Depends on retention d p
= Particle diameter (units) D m
= Diffusion coefficient of analyte in MP (cm 2/s) 1 cm 2= 10 4mm U= MP velocity |
Cs
U-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
= (f s
(K')d f
2*U)/D s
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 |
Resolution
Define Resolution |
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 |
Successful Separation |
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 |
Quantify Resolution (R/Rs
) |
Use W
Captures +/- 2𝜎 regions of "Gaussian" peaks
Corresponds to ~ 95.5% of analyte |
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R improves: Greater ∆t r
Smaller W a
and/or W b
Narrow 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 |
Resolution Diagram
Graph A-C has poor resolution Overlapping peaks
Graph D has the minimum resolution requirement
Graph E-F has a good resolution See baseline between peaks
Controlling Resolving Power
Control Resolution |
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 |
Effects of Retention and Selectivity on R' |
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) |
Effects of R' on Retention Time |
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 |
Effects on Retention and Selectivity R'
Effects of R' on tr
Notice that R’ increases significantly at low K’ but plateaus at large K’
Don’t use separations with small K’ (low R’)
Notice that tr increases linearly with increasing k’ BUT R’ plateaus at large k’
Therefore there is no real benefit to sep’ns with large k’s (b/c R’ ≈ constant)
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