Cheatography
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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 

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
Retention 
Peaks located in chromatogram 

Analyte interaction with column stationary phase: strongint. = slow rate 

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] 

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 HPcylinder + 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 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 

K' 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 
Efficiency
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 Overlapping 
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 

Desirable Narrow peaks and small volume 

"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) 

Desirable 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 fullwidth at half maximum (FWHM) establish SD 

W1/2 ≠ 1/2 W 
FullWidth at Half Maximum
Band Broadening
Occurrences 
Low efficiency Not fully separated peaks Interferences 

Dispersion is independent of retention 
Van Deemeter Overview 
ATerm Associate with multiple flow paths through column Each unique distance Result in variety of times to transit column 

BTerm Associate with longitudinal diffusion of analyte Some analyte will arrive sooner/later Depends on magnitude + direction of net diffusion during tr 

CTerm Split into 2 subterms Relate to reality that chromatogram is carried out in nonequilibrium 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) 

ATerm: Constant (purple line) 

B/UTerm: Varies as 1/U (pink line) 

Cs UTerm: Linear increasing (blue line) 

Cm UTerm: Linear increasing (yellow line) 


ATerm: 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: HAterm = 2λdp λ = quality/tortuosity factor ~0.50.6 (packed column) FSOT less 
B/UTerm: 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: HB/UTerm = (2𝛾Dm )/U Dm = Diffusion coefficient in MP 𝛾= Obstruction factor ~ 0.6 (packed column) ~ 1.0 ( open tubular column) U= MP velocity 
CTerm: Resistance to Mass Transfer
CTerm 
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: SP MP Interface 

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 
Cm UTerm: Resistance to Mass Transfer in MP 
Space inbetween 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 

Equation: HCmU = (fm (K')dp ^{2}*U)/Dm fm (K') = Quasi constant Depends on retention dp = Particle diameter (units) Dm = Diffusion coefficient of analyte in MP (cm^{2}/s) 1 cm^{2}= 10^{4}mm U= MP velocity 
Cs UTerm: 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 

Equation: HCsU = (fs (K')df ^{2}*U)/Ds df = SP thickness Ds =Diffusion Coefficient of analyte in SP 

GC: ~0.10.5 µm film thickness Controls retention Impact resistance to mass transfer 

LC: Never adjust to thickness Monolayer Resistance Negligible Important in MP 
Resolution
Define Resolution 
2 peaks of interest (critical pair) Peaks closest together 

Resolved 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 AC has poor resolution Overlapping peaks
Graph D has the minimum resolution requirement
Graph EF 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 

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 

Interplay between R' and tr as a function of K' 

R': N and 𝛼 ~ constant when K' is alter Replace terms with Q 

trb : 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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