SEPARATIONSCIENCESERIESEditors: RaymondP.W.Scott andColinSimpsonQuantitativeAnalysisusingChromatographic TechniquesEdited by Elena KatzTheAnalysisof Drugsof AbuseEdited by Terry A. GoughLiquidChromatographyColumnTheoryby RaymondP.W. ScottLiquidChromatographyColumnTheorybyRaymondP.W. ScottChemistryDepartment, Birkbeck College, University ofLondon, UKandChemistryDepartment, GeorgetownUniversity, WashingtonDC, USAJOHNWILEY & SONSChichester . New York . Brisbane . Toronto . SingaporeContentsPrefaceAcknowledgements1Introduction to the Liquid Chromatographic Column .The Factors that Control Retention and Selectivity .Ionic Interactions .Polar Interactions .D . Itt'lsperslve n eracIons .The Physical Nature of the Column .. , .The Column Environment .Chromatography Nomenclature .LC Column Theories .References .2The Plate Theory .The Solution of the Differential Equation .The Retention Volume of a Solute .The Capacity Ratio of a Solute .The Separation Ratio .References .3The LC Column Dead Volume .References _ .4Extensions of the Plate Theory .The Elution Curve of a Finite Charge .Peak Asymmetry .IXXl1445568912131519222526262738393941'IColumn Efficiency 45The Position of the Points of Inflection 48The Gaussian Form of the Elution Equation 50References 525Applications of the Plate Theory .. . . . . . .. . .. . . .. . .. . . . . .. . . . . . . . . . . . . .. . . . . . 53The Maximum Sample Volume 53Vacancy Chromatography........ 55The Resolving Power of an LC Column 60The Effective Plate Number 63The Peak Capacity of a Chromatographic Column 67Precision as an Alternative to Resolution 74A Theoretical Treatment of theHeat of Adsorption Detector 77References 906Introduction to the Rate Theory . .. . . . . . .. . .. . . .. . .. . . . . . . . . . . . . .. . . . .. . . . . . 93The Summation of Variances 94Extra Column Dispersion 95The Alternative Axis of a Chromatogram 96The Random Walk Model " . . . .. . .. . . .. . . . . . . . . . . .. . . . .. . . . . . 98Dispersion Processes that take Place in an LC Column 102The Multipath Process 102Longitudinal Diffusion 103The Resistance to Mass Transfer in the Mobile Phase 105The Resistance to Mass Transfer in the Stationary Phase . . .. . . . . . 106References 1067The Van Deemter Equation . .. . . . . . . . .. . . .. . . .. . .. . . .. . . . . . . .. .. . . . . .. . .. . . . . 109References 1218Alternative Equations for Peak Dispersion 123The Giddings Equation 123The Huber Equation 124The Knox Equation 126The Horvath and Lin Equation . . . . . . . . .. .. . . . .. . .. . . . . .. . . . . . .. . . . . .. . . .. . . 128The Golay Equation 128References 1339Experimental Validation of the Van Deemter Equation 135The Effect of the Function of k' on Peak Dispersion 149References 15210Extra Column Dispersion .The Effect of Sample Volume .The Sample Valve , .Connecting Tubes .Low Dispersion Connecting Tubes .Serpentine Tubes " .Column Frits .Dispersion in the Detecting Cell .Effect of Extra Column Dispersion on Column Radius .Mass Sensitivity , , .References .II LC Column Design -The Design Protocol .Performance Criteria .The Reduced Chromatogram , .Instrument Constraints .Elective Variables " .Column Specifications and Operating Conditions .Analytical Specifications .12LC Column Design -The Design Process for Packed Columns .The Optimum Particle Diameter .The Optimum Column Length .The Minimum Analysis Time .The Optimum Column Radius .The Optimum Flow Rate .The Minimum Solvent Consumption .The Peak Capacity of the Optimized Column .Maximum Sample Volume .The Optimum Capacity Ratio .Packed Column Design Equations .Computer Program for Packed Column Design .Gradient Elution .References .13LC ColumnDesign - The DesignProcessfor Open TubularColumns .The Optimum Column Radius .The'Optimum Length of an Open Tubular Column .Minimum Analysis Time .The Optimum Flow-Rate .VB15315315415415816116416416717217317517617717918118218318518819219419619920120220420420620821221321521822122222417111MaximumSampleVolumeandMaximumExtraColumnD .Isperslon .The Maximum Permissible Detector Dispersion .Design Equations .The Open Tubular Column in LC ..References .14Preparative Liquid Chromatography Columns .Preparative Column Design .The Efficiency Required from the Preparative Column .Optimum Particle Diameter .The Column Length and Analysis Time .The Column Radius .The Optimum Flow-Rate .Solvent Consumption .Column Wall Thickness .Preparative Column Design Equations , .The Use of the Design Equations .ComputerProgramfor PreparativeColumnDesignD .ISCUSSlon .Column Overload as an Alternative to Column Design .Sample Volume Overload .Sample Mass Overload .References .List of Symbols .Appendix1TheDiffusionCoefficientsofsomeLowMolecularWeight Substances " .Appendix 2The Diffusion Coefficients of some Peptides226230231233234237238238239241244247248248250251252253259259261263265268270Appendix 3ThePhysical PropertiesofsomeSolventsEmployed as Mobile Phases in LC 271Index .. I .. I I .. .. I .. I .. I I I I .. I ~ .. .. .. .. .. -II .. II .. .. .. I ... .. I I .. I 273Indexadjusted retention time,definition, 11retention volume, definition, 11adsorption, detector, heat, equation foroutput, S3equation for on column detection. 87theory of, 77isotherms, 43alumina, coated stationary phase, 2limitations as anLC stationary phase, 2analysis time, approximate for packedcolumn, 117minimum, optimized open tubecolumns. 222equation fOL 223minimum. optimized, packed columns.194equation for, 195minimum, optimized, preparativecolumns, 242equation fOL 242particle diameter, 121analytical specifications for optimumcolumn, 183asymmetry, peak, 41available stationary phase, definition,30axisof a chromatogram, 96base line, definition, 10capacity peak, 67and capacity factor, 71equation for, 70optimized column, 20equation for,203ratio, 25calculated from, exclusion volume,151permeating volume, 150effect on dispersion, 149equation for, 25explicit equation for, 32cell detector, dispersion effect, 164design for low dispersion, 166volume, effective, heat of adsorptiondetector. 79charge, finite, elution curve of. 39chromatogram, axes of, 96reduced, 177chrornatorgaphy.nomenclature, 9vacancy 55 ,applications. 59equation of elution curve, 59column, capillary, 6characteristics of, 1dead volume, 10,27design, open tubular volumns, 215optimized open tube columns, 231program for, 232optimized packed columns, 206program for. 20Roptimized preparative columns. 250program for,252packed, 185 ... _, optimum particle diameter, 239diameter versus particle diameter, 171dispersion. extra, 153packed.102longitudinal diffusion. 103equation for. 104L./'fdispersion (cont.)mul tipath , 102equation fOL10.3resistance to mass transfer, mobilephase, 106stationary phase, 106environment, 8efficiency, 45equation for, 46, 47frits, contribution to dispersion. 164flowrate. defini tion ,10optimum for open tube,224optimum for packed, 199optimum for preparative, 247heat capacity, 8length, approximate for packedcolumn, 117optimum for open tube column,221equation for, 222optimum for packed column, 192equation for, 192optimum for preparative column,241equation for, 241particle diameter for maximumefficiency, 120particle limits, 8material of construction, 6open tubular, optimum, design, 215flowrate,224equation for, 225radius,218equation, 219velocity, 217minimum HETP, 217limitations. 6, 233overload, 259packed, 6optimum, specifications for. incolumn design, 182physical nature of, 6properties of Zorbax column, 37purpose of, 3quartz.availability, 7radial equilibrium, 100radius, dependance on extra columndispersion, 167equation for, 169, 170optimum, open tubular,218equation for. 219packed, 196equation fOL198preparative, 244equation for, 246resolving power, 60equation fOL 62the ories , 12thermostat. 8volume, total, expression for, 28wall thickness, limitations. 8preparative, 248weight, limits, 8computer program for the design of opentube columns, 232report for a packed column design, 233computer program for the design ofpacked columns, 208report for a packed column design,210computer program for the design ofpreparative columns, 252report for a packed column design. 256connecting tubes, dispersion, cause. 154equation for, 155length versus variance, 157low dispersion, 158coiledtubes, 159Hiu curves, 161serpentine tubes, 161H!ucurves, 162. 163pressure drop across, 156constraints. instrument,in columndesign, 179criteria for column performance. 176dArcys law. 116dead,point, definition. 10time definition, 10volume, definition, 10discussion of, 27kinetic, 31thermodynamic. 32design. equations for open tube columns,231program for. 232equations for packed columns, 206program for. 208equations for preparative columns, 250program for, 252open tubular columns. 215packed columns, 185preparative columns. 237protocol for columns. 175detector, cell, design for low dispersion,166dispersion, effect on, 164heat of adsorption, theory. 77equation of output, 83equation for on column detection,87differential equation for the elutioncurve, 18diffusion coefficients, list of,268peptides 270diffusivity relation to, longitudinaldiffusion, 143minimum HETP, 145resistance to mass transfer, 147dipole, induced, 5interactions. 5dispersion, detector cell dispersion,effect on, 164effect of sample volume, 153extra column. 6, 95, 153packed column, 102radial, 99equation for, 100dispersive forces. 5dispersive interactions, 5distribution, 4coefficient. 16factors controlling, 4effective. cell volume, heat of adsorptiondetector. 79plates. 63equation for, 64relation toequilibrium plates. 65efficiency, column. 45equation for. 40.4.7particle diameter for a packed column.119radius for an open tube column. 132elective variables in column design. 1K1elution curve equation, 19.21derivation. 16finite charge, 39Gaussian form, 50equation for. 52solution of differential form. 19gradient. 213profile. of iowa ~ p e c l ratioLUbe. i65environment. column. 8equation. dArcys.fluidflow through apacked bed. 116design for optimized packed column,200i./.Jefficiency required toeffect a givenseparation, 62elution curve. 19.21derivation. l6Gaussian form, 50equation of. 52finite charge, 39, 40Giddings. dispersion ina packedcolumn, 123Golay, for dispersion on open tubes.128heat of adsorption detector, ~ 3with on column detection. 87Huber. for dispersion ina packedcolumn. 124Horvath andLin, for dispersion in apacked column, 128Knox. for dispersion in a packedcolumn. 126mass sensitivity. 172Poiseuillcs , fluid flow through a tube.132Van Deernter, 109detailed, 110equilibrium, radial, column. 100extra column dispersion. 6, 95,153effect on column radius, 167factors that control retention andselectivity. 4finite charge, elution curve of, 39flowrate, definition, 10for optimized open tube column.224equation for. 224for optimized packed column. 199equation for. 199for optimized preparative column. 247equation for. 247frits. column. contribution to dispersion.164Giddings. equation for dispersion inapacked column. 123Golay, equation for dispersion in opentubes. 128gradient elution, 212heat of adsorption detector. equation ofoutput. 84equation for on-column detection, 87theory. 77height. peak. definition. 11LibHETP. curve. for open tubes, 129for packed columns. IIIvan Dccmtcr, 138definition of. 97equation. for an open tube column. 128for a packed column. 110for an open tube. uncoated. 129minimum, dependance ondiffusivitv.145packed column. 115open tube column. U 1.217Horvath and Lin. equation for dispersionin a packed column. 128Huber. equation for dispersion in apacked column. 124induced dipoles. 5inflexion points, of elution curve. 48equation for. 49injection point. definition. 9instrument constraints. in column design.179interstitial volume. definition of. andexpression for. 29effect of ion volume of marker,34-static, 29. )9movmg. _ion volume. effect on interstitial volume.34ionic interactions, 4isotherms. adsorptions. 43effect on peak shape. 44kinetic dead volume. 31Knox. equation for dispersion in apacked column. 126length. column, approximate for packed,117optimum, foropen tube. 221equation for.221optimum, forpacked. 192equation for. 1prr1:=,p :=.y=;temisusedon twocolumns, andthesolutesarecbrornatoqrapheoat Hie sametemperature, then thetwo solutes willhave the same separatIon rat i 0onbothco1umns. Theseparati on rat i 0 will beinde{Jendentof the phase rsttasof thetwoco lumnsandthe flow-rates. 1tfollows, that tneseparationratio of asolute can be used reliably as ameans of solute identifIcation.A standard substance isoftenadded to a mixture andthe separationratioofthesubstance of interest to thestandard 1s used for ident 1rtcat ion. Inpractice theseparation ratio is taken as the ratio of the distances Incentimeters between the dead point and the maximumof each peak. Ifcomputer data processing is being employed replace distances bycorresponding times.References(1) AJ.P. Martin andR.L.SyngeJ8/ocIJem. J. 35( 1941)1358(2)" Gas CIJromato.qrapl7yc:o-1,.Jc:Q),.JQ)Ct:o 300C 500C40 10 20 30Carbon NumberO+-....,.........,...--.......-----------..----foIt is seenthat an approximately linear relationship exists between theretention volume of eachalkaneanditscarbonnumberandthat the smallermoleculeexhibits thegreatest retention. Thisis adirect result of theexc1usi on propert i esofthesil i cage1support. Thefact that the data, takenat the twodifferent temperatures, fallonthe samestraight 1ineconfirmsthat little or no partition is taking place and that the difference inretention between the individual solutes is entirely related to theirmolecular size.It followsthat retentionmeasurementsonsilicabasedstationary phasesfor' HIe purpose of obtaining thermodynamic data is fraught withdifficulties. Data from solutes of different molecular size cannot becomoareoor related to otherinteract ing vari ables Ideally) thermodynamicmeasurementsshouldbemade on columns that contain stationary phasesthat exhibit noexclusion oropert ies, However, theonlycolumnsystemthatmightmeet thisrequirement isthecapillary columnwhich, unfortunatelyintroduces other complicatrons wrncn wlil be discussedlater,The bestcomororntsefor si 1ica basedstat ionaryphasesistouse correctedretention volume data for solutes eluted at a Ck') ofgreater than5andonly37compare chromatograph1c data for solutes of approximately the samemolecular size.A summaryofthedataforthe Zorbaxcolumnobtainedby Alhedai etal isshown1n Table2.Table2Summaryof thePhys1cal and Chem1cal Propert1esof theZorbaxcolumn2,79ma,87ml2,78ml2.77mla,70ml0,18ml1. 91 mllAlmlO.SOmlColumn Length 25cmColumn Radius 2,3mmColumn Piking Zorbax C8 Reverse Phasecarbon Content of Reverse Phase 1O . O ~ w / wEquivalent Decane Content (dimethyl octene) 11, 8 ~ w / wTotal Column Volume 4.15mlTotal Volume of Silica in the Column 0,96mlTotal Volume of Stationary Phase in the Column OAOmlVolume of Chromatographically Available Stationary Phase OA9mlVolume of Chromatographically Unavailable Stationary Phase (by difference)Total Mobile Phase in the column.11 By Weighing21 From the Retention of the alkanes in n-Octens extrapolatedtoan alkane carbon number of 33/ From the volume frition average of the isotopes retentionvolumeTotal Interstitial Volume. Value extrapolated fromthe retentionvolumes of ions of different size.Interstitial Moving Phase Volume. From the Retention of 'SilicaSmoke'Interstitial Static Phase Volume.By DifferenL1lTotal Pore Volume. By DifferenL1lPore Volume Containlng Components of the Moblle Phase of Dlfferentcomposition tothat of that of the Moving Phase,( bydifference)Pore Volume Containing Mobile Phase of the same compostnon as theMoving Phase, (by differenL1l)

It 1S seen that the otstrtbutron of the vartous chromatograph1callyimportant volumeswtthtnanLCcolumnISnetther strr.olenor' obvtous. it isalso seen that about 70%of thecolumnvolume1S occuotecby rnobtlephasebut onlyabout 50%of that mobile phase 1S actually moving, Furthermoreabout 18% ofthe mobtle phaseistntersttttal but staticandabout 31 %of themobilephase 1ScontainedWithinthe pores and 1Salsostat 1C. Just over 6%of HIemobilephase1nthe poreshasa d1fferent compositiontothat of themotnlephase proper and UIUS constitutes asecond stat i onary phase Thestattonarv chase canstitutes about 12%of the co lumnvolumewhich isecuivaienttoabout 17% ofthe rnoonephase content of the column.Thevalues givenintable(2) areprobablyrepresentative of most reversephase columns but may differ signHicantlyfromsihca gel columns.References( 1) H. lnge Irlardt,H.MullerandS, Dreyer, aromstoorsonr, 19( 1984)240.(2)PL,L'lIrorl7atogra,01J13, 20( 1985)425.(3) J.H, KnoxandR. J. kaIi szanJ./ (lIrorl7atogr , 349( 1985)211.(4) R.J. SmithandC. S. N1eassJ ./ L/q. CIJromatogr: J9( 1986)1387.(5) H. CoUn, A.JI I II n 1 I J"""""II =Vo , lL.--nkgS-nkAOWS---",I II : =lItisinterestingto note that, althoughthestraight tubetheoryof GOlayisnotappliedtocoiledtubes, hisequationcanbeemployedtoqualitativelyexplain the shapeof thecurves given infigure 2. At lowvalues of themobilephase velocitythe effect of longitudinal diffusiondominates) butasthe velocity tends to approachthe optimum, the resistance to masstransferterm begins to increase and the value of (H)also rapidly increases.Figure2CurvesRelat tnq(H)agaInst(u) for DIfferentCol1edTubesMOBILEPHASE,' 5%ETHYLACETATEinn - HEXANESOLUTE,' BENZYLACETATE2.5Eu 2.0a..I-wI 1.51.0uCOILOTUB .,ICOILED TUBE#2COILED TUBE #3COILOTUBE #4However, at higrl velocities theeffectivevalueof thectrrustvtty of thesolute dramaticallyincreasesasa result of inducedradial flow} eventually. reducing HIe resistanceto mass transfer factor toVirtually zero, Thisresultsin a corresponding dramatic reductionin the valueof(H), Finally) atvery high velocit ies, thegreatlyreducedlongi tuci naI diffus ioneffect agai ndominates. At this point, the value of (H) is very small and, in fact,decreaseseven furtheras the mobile phase velocityis turther Increased,Serpent ine TubesThe 10\,,-/ dtsperstonserpentinetube developedbykatzft8/. (10) was analternative approach to the coiled tube and was designed to increasesecondary flow by actually reversIngthe direction of flow at eachserpentine bend, Adiagram of a serpentine tubeisshownin figure3. In fact}theserpentinetUbingshowninfigure 3was designed tobe an interface162between aliquidcbromatoqrapb and an Atorntc Adsorption Spectrometer.Theserpentinetubeis encasedinan outer sheathtoprotect thetubeandprovtdesome rigidity.Figure 3The LowDtsperston Serpentine TubeDimensions: (r), (internal), 0.0127cm(0.010in. 1. OJ(n, (externa1), 0.025 cm (0.020 in O. DJ(U, length (linear) 42.5 cm.(]), length (cotl) 38.5cm.(5), (serpenti ne ampl i tude) 0.05cm.Figure 4Graphs of PeakVariance aga1nstFlow Rate forCoiled andSerpentj ne Tubeso Coiled Tube Cr=O.O13 em,I=337.5 em.d(coll)=O.996mm) ZlgZ.g Tub. (r=O.O13 em.I=42.46em)-Eu........N

-I:-D: 020.,.,..Docuc:':: 0-05>o 10 2-0 3-0-Fla. R.te Iml/mln\4'016'A graphrelatlngthe varianceper untt lengthof thetube(H) against flowrateis shown in figure 4}fora serpentinetube havingthedimensionsgivenin figure3.The flowrate is employedas themdepencentvariable) analternativetothemoreusual linear velocity, asthe flowrateisdefinedby thecolumnwithwhichthelow dispersion tUblng1S to be used It will beshowninduecoursethat the column flowrateis independently defined by thenature of theseparationthat istobe achievedbythe column. It isseenthat a similarcurve is obtained forthe serpentine tube, as that forthe coiled tuoe.butthethemaximumvalueof (H) isreachedat a muchlowerflowratethanthatwith the coiled tube. Furthermore) thevariance remains more or lessconstant over awiderange of flowrates that encompass those usuallyemployedin normal LC separat ions.Figure5Graphs of PeakVarianceagainstFlowRatefora straight andSerpentineTube',5-Eu... ING "#.###"; V,LPRINT"mI"LPRINT"PeakcapacityLPRINTUSING n#:tt##". NIIIIIf the proqrarnis run on aMacintoshcomputer, thenitwill start processingimmediately, However, it will obviously notcomplete the programuntil thelast entryis made(thevalueof theextracolunnotsoerstoni Thedataisentered sequent ially on request fromstatements given on HIe computerscreen.On completion, HIe results are sent totheprinter andanexamp teofa computer print out isgivenbe low.TheComputerReportPERFORMANCECRITERIAIIA defined resolution must be obtained2/ The analysts must becomp1etedin the minimum time3/The analysis must be completed wahthe mlnimum solvent"INSTRUMENTCONSTRAINTMaximumColurnnInletPressureExtra Column DispersionMUltipath Packing FactorLongitudinal Diffusion Packing FactorColumn MobilePhase Fraction"ELECTIVEVARIABLES""Separat ion Rat to of the entical Pair"Capacity Ratio of the First Peak of the Pair"Capacity Ratio of the Last Eluted Peak"Dlffusivity ofSolute in Mobile Phase"Vi scosity of nobuePhaseCOLUMN SPECIFICATIONSOpt imurnCOl umn RadiusoottmumColumn LengthOptimumParticle Diameter6000 o.s. i.0.0025 ul.5.6.651012.550,000035so.ernper sec0.023 Poises0.0197cm1577 cm46.2urn? 11ANALYTICALSPECIFI CATIONSMinimum Analysis Time 306089 secColumn Efficiency313600Optimum Flow-Rate 1.47 ul/rntnMaximumSampleVolume 8.59 ulSolvent Consumption per Analysis 7.50 mlPeak Capacity 251Table2 DesignDataon a Series ofOptimized ColumnsSeparation Parti cle Column Analysis PeakRatio Diameter Length Time Caoactty(micron) rn)1,006 385 7300 27.3 days 4191.008 28.8 3079 8.6 days 3141.010 23.1 1576 3.5 days 2511.012 19.3 913 41 hrs 2101.014 16.5 574 22 hrs 1801.016 14.4 385 13 hrs 1571.018 12.8 270 8.1hrs 1401.020 11.6 197 5.3 hrs 1261.02 10.5 148 3.6hrs 1151.026 8.9 112 111.6 min 971.030 7.7 58A 58,4 min 841.035 6.6 36.8 34.0 min 721.040 5.8 24.6 19.9 min 631.050 4.6 12.6 8.2 min 511.060 3.9 7,3 3.9 min 421.070 3.3 4.6 128sec 361.080 2.9 3.1 74.7 sec 321.100 2.3 1.6 30.6 sec 261.120 19 0,9 14.8 sec 21Notek'=2.5, k'2=5,DlffuSivlty of solute=3.5X 10-5, viscoSity=0.023POlses).,=0.5, y=0.6)=0.65and extracolumndtspersion1S taken as 0.0025~ li Lj ~ ~ e e r l lhal by the appropriale use 01 1illUid cluomatoqrapnv columntheory it ispossible todesignthe optimum packedcolumnfor any specificseparation. InHIe next chapter asimilar procedure will be adopted todevelop a regime for designing the optimumopen tubular column. The212conditionsused to obtain the data given in table 2ts fairlytypical formostLCanalyses of relauvetv small molecular weight substances, It is seen)that there isa ttmttedrangeoverwhich the operationof LCcolumnswouldbepractical. A nine meter column, packedwith20rmcronparticles) 'wouldseparate a critical pair witha separationratioofonly 1.012, but itwouldtake 41 hoursto completeananalysis. It ispossiblethat there mightbeasample of sufficient importance to spend this amount of time on theanalysis, but It 1S morelikelythat the analyst wouldseek an atternativemethod At the other extreme particleshavlng diametersless than 3 micron,althoughavailable, arecurtcutt topack, Assumingthat thepractical peakcapacityisabout half thetheoretical peakcapacity) a column3.1 ern longpacked withparticles 2,9micronindiameter would separate amixturecontainingabout 16 components In just over 30 seconds. Thisparticularcolumn is commercially avatlaole in ctose-to-oottrntzeo form (knowncolloquiallyas the 'three by trvee':andwouldprobablybe themost suitablefor n)e rapid analysis of simple mixtures, The two other common,cornmerctauyavailable) particlesizes) 5and 10 micron, shouldbepackedinto columns 12.6 and 148 centimeters 10ng respectively for optimumoertormance Suchcolumnswouldprovidea 'columnfamily' for general usewhichwouldencompassthevast majorityof LCappl tcattonsthat facetheanalyst tooav It shoulo be emphasized, however, that for arepetitiveanalysis that isrepeated many times every day) as inaquality controllaboratory, HIeconstruction ofthe fullyoourmzeocolumnthat isspectr tcforHIe particular analysis would always be econormcauvwortnwrule.Gradient ElutionThe designproceduredescribedabove will, in theory, beapplicableonlytosamples that are separated by .socrauc development. Undergradient elutionconditionsHIe (k') valuesof eachsolutearecontinuallycr,cmging, togetherwith the viscosity of themobilephaseandtheourusivitvof eachsolute inthe mobile phase, As a consequencetheequations derived fromthep1ateandratetheorles will onlybeapproximateat best andin most casesgiveverymisleading values particularly for column efficiency. As the effiCiencyrequired to separate thecritical pair is crucial to column design, theoptimum column for use 'in gradient eluttor deveiopment 1S almostimpossible to calculate,However, qradient elutionisoftenemployed, asan alternatjvetoisocraucdevelopment, tosvotaHiedesignandconstruction of theoptimumcolumnwhichis seen as a procedure Whl en can be ted lous and time consuming.Samples that contain solutes that cover awide ootar tty range, whenseparated with asolvent mixture that elutes the last component in a213reasonabletime, often fails to provideadequate resotution for thosesoluteselutedearly in the chrornatogram. For the occasional sample, gradientelutionprovidesHIebestandimmediatesolutiontothisproblem. However,for oualttvcontrot, where there is ah1gh dally throughput of samples,tsocratic development, employedinconjunctionwith anoourntzeccolumn.1Slikelytobemoreeconomic In manyapplications, theoptrmizcdcolumn,operated tsocrattcauv, will provide ashorter analysis time than thatobtained byqradrent elution used With an adooc column Furthermore,tsocratic developrnent eliminatesthetime required after gradient elutiontobring the columnbackto equillbriumwith the inlt1al solvent mixturebeforecommencing thenext analysis. Excluding samples of biological orq!n,isocraticdevelopment isthepreferredmethodfor routineLCanalysisas,winl anopurntzeocolumn. it is usuallyfaster, utuizes lesssolvent andreouires 1essexpensive appar atus.Samplesof biological originfall ina classof their own. Many blologica1samples canbe separateo by gradlent elution particularly thernacrornotecules, polvpeptides, proteinsetc However, duetothenature ofthe samples. the gradient isoftenverysmall indeedasa suqnt charqeinmobile phasecomposition can make adramatic change inelution rate ofmany rnacrorno1ecui es. Consequently, the solvent viscosity and solutediffusivitydoesnot ctianqe significantly duringthe programand, for' thepurposesof columndesign, thecrromatocrarn can be treatedathough theseparatton was deve1ope(j isocratical1y and separation ratios capac-tvratiosand efficiencles calculated in the normal wayReferences(1) J. H. Purnell, Nature.No.4704,Dec, 9,( 1959)2009,(2)J.JVan DeernterJ.J.Zuider'wegand AKlinkengerg, CIJemEng,5ci,S( 1956)24(3)J C. G1ddJngs,olf.77romatograjJlJ,J1, Marcel Dekker,NewYork.t 1965) 56,(4) J A. Riddick andW. 8. Bunger, O(qan/c.Jorm VIneyandScns,NewYork,Sydneyand Toronto (Chapter 13LCCOLUMNDESIGN-THEDESIGNPROCESSOpenTubularColumnsIn a sirrnlar mannertothe designprocessfor lx/eked COIUf17n.5., theprlYSlcalcnaractensucs and the oertorrnence soecincattons can bE' calculatedtneoret i cally for theope() tubular COIUfl7/)S Again, tneproceour elnvolvestheuseofa numberof ecuattons that havebeenprevioustvoer iveoand/ordtscussed(1). However! it wi 11 be seenthat as a resul t of the qeometr i cstmphcttvof theopentubularcolumn, thereare nopackingfactors and nornultipatf termand soHIeequationsthat result arerar lesscomplex andeasier to manipulateamJ to understand,The baSICstartingequation 1S againthat of Purnell (2) wrncn auowsthenumber of theoreti cal plates requi red to separate the cr tt i ca1pair ofsolutes tobe caicutated...... ."" ' ,... (1)where(0) is the separation rat i 0 of the crit tea1pair,and (k'p)isthe capacity ratio ofthe first eluted peakof the critical pair.The next equation of importanceistherelationship between the columnlengt.h(J), andtlle height of the theoretical plate(H),1 =nH , , , " (2)where (n) 15 thecolumn etr ictencyas defined in eouauon (1)216 J '-J11 I t:\ ,r\ i r l-J"I -; ('; \ 1.'", ,'" r-.," ,", . 'r- .', I I I I -, \ j I L'''J_ '" J ,I, ..... .jI 1BH=- +Cuuwhere: (u) istrwltnear vetoc.tvof the moouephaseand (8)and(C)are constants(3)Now, B =2Dm( 4)where(Drn), isHie DlffuSivltyof the solutem the mobilephaseandc=(1+6k+11k'2)r224(1+k,)20m1