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% Document Info
\author{shaylannxd}
\pdfinfo{
  /Title (chromatography-theory.pdf)
  /Creator (Cheatography)
  /Author (shaylannxd)
  /Subject (Chromatography Theory Cheat Sheet)
}

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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Chromatography Theory Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{shaylannxd} via \textcolor{DarkBackground}{\uline{cheatography.com/149855/cs/32519/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}shaylannxd \\
  \uline{cheatography.com/shaylannxd} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 14th June, 2022.\\
   Updated 19th June, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
\raggedright
\raggedcolumns

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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{{\bf{Separation Theory}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Analyze Complex mixtures}} & \{\{nobreak\}\} If analyte produce overlapping signals \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Process of unmixing a sample}} & Input energy \{\{nl\}\}Analyte are diluted \tn 
% Row Count 5 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Requirements}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Stationary Phase (SP)}} & Fixed in column \{\{nl\}\} Interacts with analyte \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Mobile Phase (MP)}} & Moves through/over SP \{\{nl\}\} Carries analyte \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Interactions}} & No interaction with SP \{\{nl\}\} \{\{fa-caret-right\}\} Travel same speed as MP \{\{nl\}\} \{\{fa-caret-right\}\} No retention = No separation \tn 
% Row Count 10 (+ 6)
% Row 3
\SetRowColor{white}
 & Interaction with SP \{\{nl\}\}\{\{fa-caret-right\}\} Analyte are retained \{\{fa-arrow-right\}\} Dispersion \{\{nl\}\} \{\{fa-caret-right\}\} Part time in SP (v=0) and MP (same speed) \tn 
% Row Count 17 (+ 7)
% Row 4
\SetRowColor{LightBackground}
 & All analyte spends same amount of time in MP but diff. time in SP \tn 
% Row Count 20 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.08 cm} x{5.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Fundamental Processes}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Retention}} & Peaks located in chromatogram \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & Analyte interaction with column \{\{nl\}\} \{\{fa-caret-right\}\} stationary phase: strongint. = slow rate \tn 
% Row Count 6 (+ 4)
% Row 2
\SetRowColor{LightBackground}
 & Control by thermodynamic property \{\{nl\}\} \{\{fa-caret-right\}\} alter property = alter retention \{\{nl\}\} Example: \{\{nl\}\}\{\{fa-caret-right\}\}Temperature (GC) \{\{nl\}\} \{\{fa-caret-right\}\} MP (LC) \{\{nl\}\} \{\{fa-caret-right\}\} SP \{\{nl\}\} \{\{fa-caret-right\}\} Analyte \tn 
% Row Count 15 (+ 9)
% Row 3
\SetRowColor{white}
{\bf{Dispersion}} & Band Broadening \{\{nl\}\} \{\{fa-caret-right\}\} peak width \{\{nl\}\} \{\{fa-caret-right\}\} how dilute \{\{nl\}\}  Ex:  \{\{fa-arrow-up\}\} Dispersion = \{\{fa-arrow-up\}\} Intensity = \{\{fa-arrow-up\}\} {[}Analye{]} \tn 
% Row Count 22 (+ 7)
% Row 4
\SetRowColor{LightBackground}
 & Depends on structure of column \{\{nl\}\} \{\{fa-caret-right\}\} \{\{fa-arrow-up\}\} Analyte mix = \{\{fa-arrow-up\}\} Dispersion \tn 
% Row Count 26 (+ 4)
% Row 5
\SetRowColor{white}
 & Depends on diffusion of analyte \{\{nl\}\} \{\{fa-caret-right\}\} \{\{fa-arrow-up\}\} Diffusion Coefficient = \{\{fa-arrow-up\}\} Dispersion \tn 
% Row Count 31 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
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\begin{tabularx}{8.4cm}{x{2.08 cm} x{5.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Fundamental Processes (cont)}}  \tn
% Row 6
\SetRowColor{LightBackground}
 & Depends on total time in column \{\{nl\}\} \{\{fa-caret-right\}\} \{\{fa-arrow-up\}\} Time \{\{fa-arrow-up\}\} Diffusion = \{\{fa-arrow-up\}\} Dispersion \tn 
% Row Count 5 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Separation Process}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Occurs in tube/plate (TLC)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Drive MP through column \{\{nl\}\}\{\{fa-caret-right\}\} consistent velocity \{\{nl\}\}\{\{fa-caret-right\}\} Use a pump (LC) \{\{fa-arrow-right\}\} HPLC \{\{nl\}\}\{\{fa-caret-right\}\} Use capillary action (TLC) \{\{fa-arrow-right\}\} Dip plate in MP \{\{nl\}\}\{\{fa-caret-right\}\} Use gas pressure (GC) \{\{fa-arrow-right\}\} Store MP in HP-cylinder + attach to gas regulator} \tn 
% Row Count 8 (+ 7)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Introduce sample at top of column} \tn 
% Row Count 9 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Allow MP to drive sample through/over SP} \tn 
% Row Count 10 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Detector at end (emerges vs. time)} \tn 
% Row Count 11 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Process}}  \tn
\SetRowColor{LightBackground}
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{8.4cm}{x{3.12 cm} x{4.88 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Retention}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Measure Retention (K')}} & Variables \{\{nl\}\} \{\{fa-caret-right\}\} L=Length of column \{\{nl\}\} \{\{fa-caret-right\}\} U= MP velocity \{\{nl\}\} \{\{fa-caret-right\}\} V = Analyte velocity \{\{nl\}\} \{\{fa-caret-right\}\} t`m` = retention time of MP \{\{nl\}\} \{\{fa-caret-right\}\}  t`r`=retention time of retained species \{\{nl\}\} \{\{fa-caret-right\}\} K=distribution constant\{\{nl\}\} \{\{fa-caret-right\}\} C`s`= {[}Analyte{]} in SP \{\{nl\}\} \{\{fa-caret-right\}\} C`m`= {[}Analyte{]} in MP \tn 
% Row Count 17 (+ 17)
% Row 1
\SetRowColor{white}
 & t`r` \{\{fa-arrow-right\}\} use to identify analyte \tn 
% Row Count 19 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & Simple matrix \{\{fa-arrow-right\}\}1\textless{} K' \textless{}10 \tn 
% Row Count 21 (+ 2)
% Row 3
\SetRowColor{white}
 & Complex matrix \{\{fa-arrow-right\}\} 0.5\textless{} K' \textless{}20 \tn 
% Row Count 23 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & K' \{\{nl\}\} \{\{fa-caret-right\}\} Determined by chromatogram\{\{nl\}\} \{\{fa-caret-right\}\} Controlled by equillibrium \{\{nl\}\} \{\{fa-caret-right\}\} Judge separation by the last peak retention value \tn 
% Row Count 31 (+ 8)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.12 cm} x{4.88 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Retention (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
{\bf{Control Retention}} & Connect to K \tn 
% Row Count 2 (+ 2)
% Row 6
\SetRowColor{white}
 & Control by thermodynamic property \{\{nl\}\}\{\{fa-caret-right\}\} Adjust temperature\{\{nl\}\}\{\{fa-caret-right\}\}Adjust type of MP \{\{nl\}\}\{\{fa-caret-right\}\}Adjust "strength" of MP/SP\{\{nl\}\}\{\{fa-caret-right\}\}Add additives to MP \{\{fa-arrow-right\}\} interact with analyte, SP, MP \{\{nl\}\}\{\{fa-caret-right\}\} Velocity of MP does not alter retention \tn 
% Row Count 16 (+ 14)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Retention Equations}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655185629_Capture5.JPG}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Efficiency}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Quantify Efficiency}} & Treat chromatographic peaks like "Gaussian" peaks \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
 & Mean = Retention time \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
 & Quantify width peak \{\{nl\}\}\{\{fa-caret-right\}\} standard deviation  \{\{nl\}\}\{\{fa-caret-right\}\} peak width \tn 
% Row Count 9 (+ 5)
% Row 3
\SetRowColor{white}
 & Smaller width = better efficiency \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & Narrow peaks = Good efficiency  \{\{nl\}\}\{\{fa-caret-right\}\} Clear separation \tn 
% Row Count 15 (+ 4)
% Row 5
\SetRowColor{white}
 & Broad peaks = Poor efficiency  \{\{nl\}\}\{\{fa-caret-right\}\} Overlapping \tn 
% Row Count 19 (+ 4)
% Row 6
\SetRowColor{LightBackground}
{\bf{Peak Shapes}} & Sample volume \textasciitilde{} 1\% column volume \tn 
% Row Count 21 (+ 2)
% Row 7
\SetRowColor{white}
 & Various processes in column spread into larger volume  \{\{nl\}\}\{\{fa-caret-right\}\} Often significant \textgreater{} starting volume  \{\{nl\}\}\{\{fa-caret-right\}\} Ex: Inj.volume = 25uL and detection volume = 200uL \tn 
% Row Count 30 (+ 9)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Efficiency (cont)}}  \tn
% Row 8
\SetRowColor{LightBackground}
 & Desirable  \{\{nl\}\}\{\{fa-caret-right\}\} Narrow peaks and small volume \tn 
% Row Count 3 (+ 3)
% Row 9
\SetRowColor{white}
 & "Gaussian Peaks"  \{\{nl\}\}\{\{fa-caret-right\}\} Peak could emerge with neighbor peak  \{\{nl\}\}\{\{fa-caret-right\}\} dilution can form broadening \tn 
% Row Count 10 (+ 7)
% Row 10
\SetRowColor{LightBackground}
{\bf{Measure Efficiency}} & Variables \{\{nl\}\}\{\{fa-caret-right\}\} N = \# of theoretical plate  \{\{nl\}\}\{\{fa-caret-right\}\} H = Height of theoretical plate (HETP) \{\{nl\}\}\{\{fa-caret-right\}\} L= Lenght of column  \{\{nl\}\}\{\{fa-caret-right\}\} W = peak width at baseline  \{\{nl\}\}\{\{fa-caret-right\}\} σ = Standard deviation (unit of lenght) \tn 
% Row Count 24 (+ 14)
% Row 11
\SetRowColor{white}
 & Desirable  \{\{nl\}\}\{\{fa-caret-right\}\} \{\{fa-arrow-up\}\} N =  \{\{fa-arrow-down\}\} H =  \{\{fa-arrow-down\}\} σ \tn 
% Row Count 29 (+ 5)
% Row 12
\SetRowColor{LightBackground}
 & W range = -2τ tp + 2τ \tn 
% Row Count 31 (+ 2)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.44 cm} x{4.56 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Efficiency (cont)}}  \tn
% Row 13
\SetRowColor{LightBackground}
 & N should be consistent \{\{nl\}\}\{\{fa-caret-right\}\} t`r` and σ scale with each other \tn 
% Row Count 4 (+ 4)
% Row 14
\SetRowColor{white}
{\bf{If Baseline not Accessible}} & Baseline peak width cannot be measured\{\{nl\}\}\{\{fa-caret-right\}\} nearby overlapping peaks \tn 
% Row Count 8 (+ 4)
% Row 15
\SetRowColor{LightBackground}
 & Use upper portion of peak that is undistorted \{\{nl\}\}\{\{fa-caret-right\}\} Use full-width at half maximum (FWHM) \{\{nl\}\}\{\{fa-caret-right\}\} establish SD \tn 
% Row Count 15 (+ 7)
% Row 16
\SetRowColor{white}
 & W`1/2`≠ 1/2 W \tn 
% Row Count 16 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{"Gaussian Peak" At W}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655188136_Capture8.JPG}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Full-Width at Half Maximum}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655188022_Capture7.JPG}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Band Broadening}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Occurrences}} & Low efficiency \{\{nl\}\}\{\{fa-caret-right\}\} Not fully separated peaks\{\{nl\}\}\{\{fa-caret-right\}\} Interferences \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
 & Dispersion is independent of retention \tn 
% Row Count 7 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Van Deemeter Overview}} & A-Term \{\{nl\}\}\{\{fa-caret-right\}\} Associate with multiple flow paths through column\{\{nl\}\}\{\{fa-caret-right\}\}Each unique distance\{\{nl\}\}\{\{fa-caret-right\}\}Result in variety of times to transit column \tn 
% Row Count 16 (+ 9)
% Row 3
\SetRowColor{white}
 & B-Term \{\{nl\}\}\{\{fa-caret-right\}\} Associate with longitudinal diffusion of analyte\{\{nl\}\}\{\{fa-caret-right\}\}Some analyte will arrive sooner/later\{\{nl\}\}\{\{fa-caret-right\}\}Depends on magnitude + direction of net diffusion during t`r` \tn 
% Row Count 26 (+ 10)
% Row 4
\SetRowColor{LightBackground}
 & C-Term \{\{nl\}\}\{\{fa-caret-right\}\} Split into 2 sub-terms\{\{nl\}\}\{\{fa-caret-right\}\}Relate to reality that chromatogram is carried out in non-equilibrium state\{\{nl\}\}\{\{fa-caret-right\}\}Analyte in Mp will be out of equilibrium with those in SP (vice versa) \{\{nl\}\}\{\{fa-caret-right\}\}Some analyte will arrive at detector earlier or later than true equilibrium would predicted \tn 
% Row Count 42 (+ 16)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Band Broadening (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
{\bf{Van Deemeter Graph}} & Produce the overall curve with distinct minimum\{\{nl\}\}\{\{fa-caret-right\}\} Corresponding to N`max` and fixed L \tn 
% Row Count 5 (+ 5)
% Row 6
\SetRowColor{white}
 & Overall Plate Height:\{\{nl\}\}\{\{fa-caret-right\}\}Equation: H = A + B/U + (C`s`+C`m`)U\{\{nl\}\}\{\{fa-caret-right\}\} Sum of 4 components (red line) \tn 
% Row Count 11 (+ 6)
% Row 7
\SetRowColor{LightBackground}
 & A-Term: \{\{nl\}\}\{\{fa-caret-right\}\} Constant (purple line) \tn 
% Row Count 14 (+ 3)
% Row 8
\SetRowColor{white}
 & B/U-Term: \{\{nl\}\}\{\{fa-caret-right\}\} Varies as 1/U (pink line) \tn 
% Row Count 17 (+ 3)
% Row 9
\SetRowColor{LightBackground}
 & C`s`U-Term: \{\{nl\}\}\{\{fa-caret-right\}\} Linear increasing (blue line) \tn 
% Row Count 20 (+ 3)
% Row 10
\SetRowColor{white}
 & C`m`U-Term: \{\{nl\}\}\{\{fa-caret-right\}\} Linear increasing (yellow line) \tn 
% Row Count 23 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Van Deemter Graph (copy)}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655237302_Screen Shot 2022-06-14 at 4.07.15 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{{\bf{A-Term: Multipath Band Broadening}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{All molecules start at top of column} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{As they move down \{\{nl\}\}\{\{fa-caret-right\}\} Follow different paths through particles\{\{nl\}\}\{\{fa-caret-right\}\}Irrespective of interaction with SP} \tn 
% Row Count 4 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Range of paths depends on size of particles\{\{nl\}\}\{\{fa-caret-right\}\} \{\{fa-arrow-up\}\} Size = \{\{fa-arrow-down\}\} \# of paths = \{\{fa-arrow-up\}\} Path length} \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Depends on how "packed: the bed is\{\{nl\}\}\{\{fa-caret-right\}\} Crack, voids, etc} \tn 
% Row Count 9 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Equation: \{\{nl\}\}\{\{fa-caret-right\}\} H`A-term`= 2λd`p`\{\{nl\}\}\{\{fa-caret-right\}\} λ = quality/tortuosity factor \{\{nl\}\}\{\{fa-caret-right\}\} \textasciitilde{}0.5-0.6 (packed column) \{\{nl\}\}\{\{fa-caret-right\}\} FSOT less} \tn 
% Row Count 13 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{A-Term Diagram}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655236320_Screen Shot 2022-06-14 at 3.51.25 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{{\bf{B/U-Term: Longitudinal Diffusion}}}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{All molecules start at top of column} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{As they move down \{\{nl\}\}\{\{fa-caret-right\}\} Molecules moves away from each other \{\{nl\}\}\{\{fa-caret-right\}\} Process continues as long as they remain in column} \tn 
% Row Count 5 (+ 4)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Dispersion in all 3 directions\{\{nl\}\}\{\{fa-caret-right\}\}Only longitudinal dispersion impacts peak width (\{\{fa-arrow-up\}\} and \{\{fa-arrow-down\}\})} \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Packing column \{\{nl\}\}\{\{fa-caret-right\}\} Reduce longitudinal diffusion = \{\{fa-arrow-down\}\} Plate height (Beneficial)\{\{nl\}\}\{\{fa-caret-right\}\}Blocks molecules travel} \tn 
% Row Count 12 (+ 4)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Equation: \{\{nl\}\}\{\{fa-caret-right\}\} H`B/U-Term` = (2𝛾D`m`)/U  \{\{nl\}\}\{\{fa-caret-right\}\} D`m`= Diffusion coefficient in MP  \{\{nl\}\}\{\{fa-caret-right\}\}𝛾= Obstruction factor \{\{nl\}\}\{\{fa-caret-right\}\} \textasciitilde{} 0.6 (packed column) \{\{nl\}\}\{\{fa-caret-right\}\} \textasciitilde{} 1.0 ( open tubular column) \{\{nl\}\}\{\{fa-caret-right\}\} U= MP velocity} \tn 
% Row Count 19 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{B/U-Term Diagram}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655236373_Screen Shot 2022-06-14 at 3.52.25 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{C-Term: Resistance to Mass Transfer}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{C-Term}} & Ideal chromatography \{\{nl\}\}\{\{fa-caret-right\}\}  Assumption that analyte can "instantly" equilibrate between 2 phases \tn 
% Row Count 6 (+ 6)
% Row 1
\SetRowColor{white}
 & MP is always moving the analyte down \tn 
% Row Count 8 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & Analyte in leading edge of peak are always moving over SP that is deficient in analyte \{\{nl\}\}\{\{fa-caret-right\}\} Reverse for trailing edge \{\{nl\}\}\{\{fa-caret-right\}\} Out of equilibrium \tn 
% Row Count 18 (+ 10)
% Row 3
\SetRowColor{white}
 & Equilibrium established when there are analyte at: \{\{nl\}\}\{\{fa-caret-right\}\}  SP\{\{nl\}\}\{\{fa-caret-right\}\}  MP\{\{nl\}\}\{\{fa-caret-right\}\} Interface \tn 
% Row Count 26 (+ 8)
% Row 4
\SetRowColor{LightBackground}
 & Takes time for analyre to diffuse to/away from phases to match equilibrium constant \{\{nl\}\}\{\{fa-caret-right\}\} In SP \{\{fa-arrow-right\}\} Analyte gets further behind than expected \{\{nl\}\}\{\{fa-caret-right\}\}  In MP \{\{fa-arrow-right\}\} Analyte gets further ahead than expected \tn 
% Row Count 40 (+ 14)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{C-Term: Resistance to Mass Transfer (cont)}}  \tn
% Row 5
\SetRowColor{LightBackground}
 & Rise to broadening \tn 
% Row Count 1 (+ 1)
% Row 6
\SetRowColor{white}
{\bf{C`m`U-Term: Resistance to Mass Transfer in MP}} & Space in-between particles depends on particles size/diameter\{\{nl\}\}\{\{fa-caret-right\}\} Distance required for diffusion to move analyte\{\{nl\}\}\{\{fa-caret-right\}\}  Reach interface \tn 
% Row Count 10 (+ 9)
% Row 7
\SetRowColor{LightBackground}
 & Delays in reaching equilibrium depends on distances \tn 
% Row Count 13 (+ 3)
% Row 8
\SetRowColor{white}
 & Distance is proportional to size of particle \tn 
% Row Count 16 (+ 3)
% Row 9
\SetRowColor{LightBackground}
 & Equation: \{\{nl\}\}\{\{fa-caret-right\}\} H`CmU` = (f`m`(K')d`p`\textasciicircum{}2\textasciicircum{}*U)/D`m`\{\{nl\}\}\{\{fa-caret-right\}\} f`m`(K') = Quasi constant \{\{fa-arrow-right\}\} Depends on retention\{\{nl\}\}\{\{fa-caret-right\}\} d`p`= Particle diameter (units) \{\{nl\}\}\{\{fa-caret-right\}\} D`m`= Diffusion coefficient of analyte in MP (cm\textasciicircum{}2\textasciicircum{}/s) \{\{fa-arrow-right\}\} 1 cm\textasciicircum{}2\textasciicircum{}= 10\textasciicircum{}4\textasciicircum{}mm \{\{nl\}\}\{\{fa-caret-right\}\} U= MP velocity \tn 
% Row Count 35 (+ 19)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{C-Term: Resistance to Mass Transfer (cont)}}  \tn
% Row 10
\SetRowColor{LightBackground}
{\bf{C`s`U-Term: Resistance to Mass Transfer in SP}} & Space in SP depends on SP thickness \{\{nl\}\}\{\{fa-caret-right\}\} Distance required for diffusion \tn 
% Row Count 5 (+ 5)
% Row 11
\SetRowColor{white}
 & Analyte reach MP/SP interface \{\{nl\}\}\{\{fa-caret-right\}\}  Equilibrium reach\{\{nl\}\}\{\{fa-caret-right\}\} Delays depends on distances \tn 
% Row Count 12 (+ 7)
% Row 12
\SetRowColor{LightBackground}
 & Equation: \{\{nl\}\}\{\{fa-caret-right\}\} H`CsU`= (f`s`(K')d`f`\textasciicircum{}2\textasciicircum{}*U)/D`s` \{\{nl\}\}\{\{fa-caret-right\}\} d`f`= SP thickness \{\{nl\}\}\{\{fa-caret-right\}\} D`s`=Diffusion Coefficient of analyte in SP \tn 
% Row Count 21 (+ 9)
% Row 13
\SetRowColor{white}
 & GC: \{\{nl\}\}\{\{fa-caret-right\}\} \textasciitilde{}0.1-0.5 µm film thickness\{\{nl\}\}\{\{fa-caret-right\}\} Controls retention \{\{nl\}\}\{\{fa-caret-right\}\}Impact resistance to mass transfer \tn 
% Row Count 29 (+ 8)
% Row 14
\SetRowColor{LightBackground}
 & LC: \{\{nl\}\}\{\{fa-caret-right\}\} Never adjust to thickness \{\{fa-arrow-right\}\} Monolayer \{\{nl\}\}\{\{fa-caret-right\}\}Resistance\{\{fa-arrow-right\}\} Negligible \{\{nl\}\}\{\{fa-caret-right\}\} Important in MP \tn 
% Row Count 39 (+ 10)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{C`m`U and C`s`U Term Diagram}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655236255_Screen Shot 2022-06-14 at 3.50.21 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Resolution}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Define Resolution}} & 2 peaks of interest (critical pair) \{\{nl\}\}\{\{fa-caret-right\}\} Peaks closest together \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
 & Resolved \{\{nl\}\}\{\{fa-caret-right\}\} Clear separation \{\{nl\}\}\{\{fa-caret-right\}\}No analyte mixing \{\{nl\}\}\{\{fa-caret-right\}\}Pure peaks \tn 
% Row Count 10 (+ 6)
% Row 2
\SetRowColor{LightBackground}
 & W is not affected by plate height \tn 
% Row Count 12 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{Successful Separation}} & Isolated peaks \tn 
% Row Count 14 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & See baseline between peaks \tn 
% Row Count 16 (+ 2)
% Row 5
\SetRowColor{white}
 & Dependent on resolution \tn 
% Row Count 18 (+ 2)
% Row 6
\SetRowColor{LightBackground}
 & Can use ruler to see if baseline from beginning/end match to baseline between peaks \tn 
% Row Count 22 (+ 4)
% Row 7
\SetRowColor{white}
{\bf{Quantify Resolution (R/R`s`)}} & Use W \{\{nl\}\}\{\{fa-caret-right\}\} Captures +/- 2𝜎 regions of "Gaussian" peaks \{\{nl\}\}\{\{fa-caret-right\}\} Corresponds to \textasciitilde{} 95.5\% of analyte \tn 
% Row Count 29 (+ 7)
% Row 8
\SetRowColor{LightBackground}
 & R improves: \{\{nl\}\}\{\{fa-caret-right\}\} Greater ∆t`r`\{\{nl\}\}\{\{fa-caret-right\}\} Smaller W`a` and/or W`b`\{\{nl\}\}\{\{fa-caret-right\}\}  Narrow peaks = more baseline expose \tn 
% Row Count 37 (+ 8)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Resolution (cont)}}  \tn
% Row 9
\SetRowColor{LightBackground}
 & Full W of peak does not matter \{\{nl\}\}\{\{fa-caret-right\}\} Only back half (peak 1) and first half (peak 2) \tn 
% Row Count 5 (+ 5)
% Row 10
\SetRowColor{white}
 & 2 neighbouring peaks are resolved when \{\{fa-arrow-right\}\} R ≥1.5 \tn 
% Row Count 8 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Resolution Diagram}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655237089_Screen Shot 2022-06-14 at 4.02.59 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Graph A-C has poor resolution \{\{fa-arrow-right\}\} Overlapping peaks \newline Graph D has the minimum resolution requirement  \newline Graph E-F has a good resolution \{\{fa-arrow-right\}\} See baseline between peaks}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Resolution Equation}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655237557_Screen Shot 2022-06-14 at 4.11.48 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Controlling Resolving Power}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Control Resolution}} & Proximity of 2 peaks is important to R \{\{nl\}\}\{\{fa-caret-right\}\} Controlled by separation conditions \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
 & Quantify proximity: \{\{nl\}\}\{\{fa-caret-right\}\} Selectivity factor \{\{fa-arrow-right\}\} Define as a ratio of distribution constant of 2 peaks \tn 
% Row Count 12 (+ 7)
% Row 2
\SetRowColor{LightBackground}
 & Peaks shares column \{\{fa-arrow-right\}\} Same SP and MP \tn 
% Row Count 15 (+ 3)
% Row 3
\SetRowColor{white}
 & 𝛼 = ratio of retention factors \{\{nl\}\}\{\{fa-caret-right\}\}  Access from chromatogram\{\{nl\}\}\{\{fa-caret-right\}\} Change in selectivity = change in resolution \tn 
% Row Count 23 (+ 8)
% Row 4
\SetRowColor{LightBackground}
{\bf{Effects of Retention and Selectivity on R'}} & Key variable that controls potential resolutions \{\{nl\}\}\{\{fa-caret-right\}\}  Resolving power (R') \tn 
% Row Count 28 (+ 5)
% Row 5
\SetRowColor{white}
 & R' dependent: \{\{nl\}\}\{\{fa-caret-right\}\} Very sensitive to selectivity (𝛼)\{\{nl\}\}\{\{fa-caret-right\}\} Somewhat sensitive to retention (K') \{\{nl\}\}\{\{fa-caret-right\}\} Moderately sensitive to efficiency of column (N)\{\{nl\}\}\{\{fa-caret-right\}\} Choice of column \{\{nl\}\}\{\{fa-caret-right\}\} Choice of MP (LC only) \tn 
% Row Count 43 (+ 15)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Controlling Resolving Power (cont)}}  \tn
% Row 6
\SetRowColor{LightBackground}
 & 𝛼 control by: \{\{nl\}\}\{\{fa-caret-right\}\} Differential interactions between: Analyte\{\{fa-arrows-h\}\} MP\{\{fa-arrows-h\}\}SP \tn 
% Row Count 6 (+ 6)
% Row 7
\SetRowColor{white}
 & N control by:\{\{nl\}\}\{\{fa-caret-right\}\} Column (L) \{\{nl\}\}\{\{fa-caret-right\}\} VD equations \{\{nl\}\}\{\{fa-caret-right\}\}Type of column\{\{nl\}\}\{\{fa-caret-right\}\} SP thickness \{\{nl\}\}\{\{fa-caret-right\}\} Operating conditions \tn 
% Row Count 17 (+ 11)
% Row 8
\SetRowColor{LightBackground}
 & K' control by: \{\{nl\}\}\{\{fa-caret-right\}\} SP type\{\{nl\}\}\{\{fa-caret-right\}\}Phase Ratio (SP thickness)\{\{nl\}\}\{\{fa-caret-right\}\} MP type (LC only) \tn 
% Row Count 24 (+ 7)
% Row 9
\SetRowColor{white}
{\bf{Effects of R' on Retention Time}} & \{\{fa-arrow-up\}\} R'= \{\{fa-arrow-up\}\} Total run time \{\{nl\}\}\{\{fa-caret-right\}\} Interplay \tn 
% Row Count 29 (+ 5)
% Row 10
\SetRowColor{LightBackground}
 & Interplay between R' and t`r` as a function of K' \tn 
% Row Count 32 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Controlling Resolving Power (cont)}}  \tn
% Row 11
\SetRowColor{LightBackground}
 & R': \{\{nl\}\}\{\{fa-caret-right\}\} N and 𝛼  \textasciitilde{} constant when K' is alter \{\{nl\}\}\{\{fa-caret-right\}\} Replace terms with Q \tn 
% Row Count 6 (+ 6)
% Row 12
\SetRowColor{white}
 & t`rb`: \{\{nl\}\}\{\{fa-caret-right\}\} N,H,𝛼, U \textasciitilde{} constant\{\{nl\}\}\{\{fa-caret-right\}\} Assume R' is not changing dramatically\{\{nl\}\}\{\{fa-caret-right\}\} Replace constant terms with Q \tn 
% Row Count 15 (+ 9)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Effects on Retention and Selectivity R'}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655238475_Screen Shot 2022-06-14 at 4.25.41 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Effects of R' on t`r`}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/shaylannxd_1655238827_Screen Shot 2022-06-14 at 4.31.52 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Notice that R' increases significantly at low K' but plateaus at large K'  \newline \{\{fa-caret-right\}\}Don't use separations with small K' (low R')  \newline Notice that tr increases linearly with increasing k' BUT R' plateaus at large k' \newline \{\{fa-caret-right\}\} Therefore there is no real benefit to sep'ns with large k's (b/c R' ≈ constant)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}