Show Menu
Cheatography

# Chromatography Theory Cheat Sheet by shaylannxd

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 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 t``r``  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  t``r`` 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 W``1/2``≠ 1/2 W

### Band Broadening

 Occurr­ences Low efficiency  Not fully separated peaks Interf­erences 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 B-Term  Associate with longit­udinal diffusion of analyteSome analyte will arrive sooner/laterDepends on magnitude + direction of net diffusion during t``r`` 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 Overall Plate Height:Equation: H = A + B/U + (C``s``+C``m``)U Sum of 4 components (red line) A-Term:  Constant (purple line) B/U-Term:  Varies as 1/U (pink line) C``s``U-Term:  Linear increasing (blue line) C``m``U-Term:  Linear increasing (yellow line)

### 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 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 C``m``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 Delays in reaching equili­brium depends on distances Distance is propor­tional to size of particle 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 (cm2/s)  1 cm2= 104mm  U= MP velocity C``s``U-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 Equation:  H``CsU``= (f``s``(K')d``f``2*U)/D``s``  d``f``= SP thickness  D``s``=Diffusion Coeffi­cient of analyte in SP GC:  ~0.1-0.5 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/R``s``) Use W  Captures +/- 2𝜎 regions of "­Gau­ssi­an" peaks  Corres­ponds to ~ 95.5% of analyte R improves:  Greater ∆t``r`` Smaller W``a`` and/or W``b`` 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

### 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 MPSP 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 t``r`` as a function of K' R':  N and 𝛼 ~ constant when K' is alter  Replace terms with Q t``rb``:  N,H,𝛼, U ~ constant Assume R' is not changing dramatically Replace constant terms with Q

### 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)

## Comments

No comments yet. Add yours below!

## Add a Comment

Your Comment

Please enter your name.

Please enter your email address

Please enter your Comment.

## Related Cheat Sheets

7th Grade Physics and Chemistry Cheat Sheet