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Chromatography Theory Cheat Sheet by

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


Stationary Phase (SP)
Fixed in column
Interacts with analyte
Mobile Phase (MP)
Moves throug­h/over SP
Carries analyte
No intera­ction with SP
Travel same speed as MP
No retention = No separation
Intera­ction with SP
Analyte are retained Dispersion
Part time in SP (v=0) and MP (same speed)
All analyte spends same amount of time in MP but diff. time in SP

Fundam­ental Processes

Peaks located in chroma­togram
Analyte intera­ction with column
stationary phase: strongint. = slow rate
Control by thermo­dynamic property
alter property = alter retention
Temper­ature (GC)
Band Broadening
peak width
how dilute
Ex: Dispersion = Intensity = [Analye]
Depends on structure of column
Analyte mix = Dispersion
Depends on diffusion of analyte
Diffusion Coeffi­cient = Dispersion
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)



Measure Retention (K')
L=Length of column
U= MP velocity
V = Analyte velocity
tm = retention time of MP
tr=retention time of retained species
K=dist­rib­ution constant
Cs= [Analyte] in SP
Cm= [Analyte] in MP
tr use to identify analyte
Simple matrix 1< K' <10
Complex matrix 0.5< K' <20
Determined by chromatogram
Controlled by equill­ibrium
Judge separation by the last peak retention value
Control Retention
Connect to K
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

Retention Equations


Quantify Efficiency
Treat chroma­tog­raphic peaks like "­Gau­ssi­an" peaks
Mean = Retention time
Quantify width peak
standard deviation
peak width
Smaller width = better efficiency
Narrow peaks = Good efficiency
Clear separation
Broad peaks = Poor efficiency
Peak Shapes
Sample volume ~ 1% column volume
Various processes in column spread into larger volume
Often signif­icant > starting volume
Ex: Inj.volume = 25uL and detection volume = 200uL
Narrow peaks and small volume
"­Gau­ssian Peaks"
Peak could emerge with neighbor peak
dilution can form broadening
Measure Efficiency
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)
N = H = σ
W range = -2τ tp + 2τ
N should be consistent
tr and σ scale with each other
If Baseline not Accessible
Baseline peak width cannot be measured
nearby overla­pping peaks
Use upper portion of peak that is undist­orted
Use full-width at half maximum (FWHM)
establish SD
W1/2≠ 1/2 W

"­Gau­ssian Peak" At W

Full-Width at Half Maximum

Band Broadening

Low efficiency
Not fully separated peaks
Dispersion is indepe­ndent of retention
Van Deemeter Overview
Associate with multiple flow paths through column
Each unique distance
Result in variety of times to transit column
Associate with longit­udinal diffusion of analyte
Some analyte will arrive sooner/later
Depends on magnitude + direction of net diffusion during tr
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 Nmax and fixed L
Overall Plate Height:
Equation: H = A + B/U + (Cs+Cm)U
Sum of 4 components (red line)
Constant (purple line)
Varies as 1/U (pink line)
Linear increasing (blue line)
Linear increasing (yellow line)

Van Deemter Graph (copy)


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
HA-term= 2λdp
λ = qualit­y/t­ort­uosity factor
~0.5-0.6 (packed column)
FSOT less

A-Term Diagram

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
HB/U-Term = (2𝛾Dm)/U
Dm= Diffusion coeffi­cient in MP
𝛾= Obstru­ction factor
~ 0.6 (packed column)
~ 1.0 ( open tubular column)
U= MP velocity

B/U-Term Diagram

C-Term: Resistance to Mass Transfer

Ideal chroma­tog­raphy
Assumption that analyte can "­ins­tan­tly­" equili­brate between 2 phases
MP is always moving the analyte down
Analyte in leading edge of peak are always moving over SP that is deficient in analyte
Reverse for trailing edge
Out of equili­brium
Equili­brium establ­ished when there are analyte at:
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
Rise to broadening
CmU-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
Delays in reaching equili­brium depends on distances
Distance is propor­tional to size of particle
HCmU = (fm(K')dp2*U)/Dm
fm(K') = Quasi constant Depends on retention
dp= Particle diameter (units)
Dm= Diffusion coeffi­cient of analyte in MP (cm2/s) 1 cm2= 104mm
U= MP velocity
CsU-Term: Resistance to Mass Transfer in SP
Space in SP depends on SP thickness
Distance required for diffusion
Analyte reach MP/SP interface
Equili­brium reach
Delays depends on distances
HCsU= (fs(K')df2*U)/Ds
df= SP thickness
Ds=Diffusion Coeffi­cient of analyte in SP
~0.1-0.5 µm film thickness
Controls retention
Impact resistance to mass transfer
Never adjust to thickness Monolayer
Resistance Negligible
Important in MP

CmU and CsU Term Diagram


Define Resolution
2 peaks of interest (critical pair)
Peaks closest together
Clear separation
No analyte mixing
Pure peaks
W is not affected by plate height
Successful Separation
Isolated peaks
See baseline between peaks
Dependent on resolution
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
R improves:
Greater ∆tr
Smaller Wa and/or Wb
Narrow peaks = more baseline expose
Full W of peak does not matter
Only back half (peak 1) and first half (peak 2)
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

Resolution Equation

Contro­lling Resolving Power

Control Resolution
Proximity of 2 peaks is important to R
Controlled by separation conditions
Quantify proximity:
Select­ivity factor Define as a ratio of distri­bution constant of 2 peaks
Peaks shares column Same SP and MP
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')
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)
𝛼 control by:
Differ­ential intera­ctions between: Analyte MPSP
N control by:
Column (L)
VD equations
Type of column
SP thickness
Operating conditions
K' control by:
SP type
Phase Ratio (SP thickness)
MP type (LC only)
Effects of R' on Retention Time
R'= Total run time
Interplay between R' and tr as a function of K'
N and 𝛼 ~ constant when K' is alter
Replace terms with Q
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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