~1974 - Solute Band Spreading in Liquid Chromatography Causes and Importance

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    Band Streadins

    Chromatography is a routine sepa-ration method now used in allbranches of science. The goal in anychromatographic separa tion is tocompletely resolve th e components ofthe mixture in the shortest possibletime; much theoretical, practical,and inst rumental effort has beenspent to at tain this goal. Initially,major efforts, a t least in instrumenta-tion an d theoretical developments,were concentrated on gas chromatog-raphy; then some seven or eight yearsago, attention was given to liquidchromatography.One impor tant factor responsiblefor this development of liquid chro-matography (LC) was the realizationthat band spreading theories in LCand gas chromatography (GC) arenearly identical; consequently, someof the technology employed in GCcan be transferred to, an d utilized in,liquid systems.As a result, to atta inbetter column efficiencies, modernhigh-speed LC (HSLC) [sometimesreferred t o as high pressure ( HPL C) ]usually employs narrower columnsand smaller support particles t hanthose used a decade ago. Of course, aprice has to be paid for increased per-formance: because of smalle r packingsize, high-pressure pumps must beused t o overcome t he low permeabil i-ty (high resistance to flow of mobilephase) of such columns.This report concentrates only onchromatographic zone broadening inliquid chromatography. We describe,in a qualitative manner, t he factorsaffecting the solute zone width andtheir relation to experimental param-eters. Th e theoretical terminologyused to ascertain the processes whichtake place in the column and causethe solute zone to broaden is ex-plained and discussed, The impor-

    in liauid ChromatograDhy:Eli GrushkaDepartment of ChemistryState Univers i ty of New York at Buf fa loBuffalo, N . Y . 1 4 2 1 4

    tance of zone width in relation to sep-arat ions and resolution is discussed.Finally, a general set of rules is givenwhich should help the practitioner toimprove the efficiency of his chroma-tographic system.

    Plate Height and Plate Numbera chromatographic column. The so -lutes distr ibute themselves betweenthe stationary phase and the mobilephase according to their partitioncoefficient, K (which depends on in-termolecular forces). The partit ioncoefficient, which is defined as theratio of the solute concent ration inthe stationary phase to that in themobile phase, dete rmines the averagevelocity of each solute zone (morespecifically. it determines the velocityof the zone cen ter ). Solutes havingdifferent part ition coefficients willmove down the column a t differentvelocities, and the differential migra-tion necessary to achieve separa tion isobtained. The partition coefficient,which is a thermodynamic qua ntity,depends on the natu re of the mobileand stationary phases and on thetemperature.As solute zones pass through thecolumn, they broaden. The broaden-ing is important as it can ultimatelyaffect the resolution. It is not enoughto just pull ap art, by differentialmigration, the various solutes. Thesolute zones should be kept as narrowas possible by proper design of theexperimental system.The quantity which measures theefficiency and is related to the peakwidth is called the plate height. H, rthe height equivalent to theoreticalplate, HETP The plate height can be

    A mixture of solutes is injected into

    obtained directly from the chromato-gram:

    L is the column length, W is the peak(or zone) width a t th e base line, W1 2is the width at half the peak height,and t R is the retention time. H hasthe dimension of di stance. Since it iseasier to measure the width a t halfthe peak height rather th an a t itsbase, Equation 1 ncludes the relationbetween H and W1 2 . The constant5.54 has a theoretical basis and is re-lated to the assumption th at t he peakis Gaussian in s hape. Some workersprefer to measure the peak wid th a t5 l O A A N A L Y T I C A L CHEMISTRY, VO L . 46, N O . 6, M A Y 1974

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    Report

    Figure 1. Relation between peakwidth and resolutionA Poor e f f i c i e n cyB More e f f ic ien t system

    about 0.6 of the peak height [for aGaussian peak, this width is twicethe st andard deviation ( 2 u)]. f thiswidth is used for the computat ion ofH , then the numerical constant inEquation 1 s 4. The smaller thevalue of H, the better the system, ev-erything else being constant.Frequently, workers in the fieldmeasure the efficiency of their col-

    umn by calculating a dimensionlessquantity called the plate nu mber(N):

    From Equat ion 2, the larger the platenumber, the more efficient the sys-tem is. The plate height rather thanplate number is, however, a moremeaningful measure of the efficiencysince it is independent to a first ap-proximation of the column length,and more importantly, at least from atheoretical point of view, it can be di-rectly related to the experimentalconditions and parameters. It is rec-ommended tha t H be measured rou-tinely when evaluating chromato-graphic columns. I t is difficult to givean absolute value which Hshoul d be,but typical values may range from0.05 to 5 mm . Th e comparison in Fig-ure 1 hows in a schematic mannerthe improvement in resolution whichcan be obta ined, by keeping thepeaks narrow, for a pair of compo-nents eluted under the same condi-tions.Before describing the connectionbetween H and some of the columnparameters, the relation between theplate height and the resolution mustbe discussed.Resolution Equationthe resolution between two adjacentpeaks is defined as

    In any chromatographic technique,

    where t~ and indicate, respective-ly, retention times and peak base linewidths, with subscript 1 dentifyingA NA L Y T I CA L CHE M I S T 1

    the first eluted component and sub-script 2 identifying the second com-ponent. The retention times are func-tions of the natu re of the solute, themobile phase, the stationary phase,and of the column length, the te m-perature, and the mobile phase veloc-ity. By a judicious choice of the st a-tionary and mobile phases, a t a giventemperature one can increase the dif-ference in retention time betweent(&) and t ( R 1 )(i.e., increase the rel-ative retention a as defined in Figure2 ) and so improve the resolution.Guidelines as to the selection of pha s-es are given elsewhere by other a u-thors (1-3).The resolution equationcan be approximated in a more usefulformR s = qp-(L)+ k 2 / (G)4 )

    The derivation of Equa tion 4 can befound in any chromatography text(for example, Appendix 2 of ref. 3 ) .The capacity ratio k, the relative re-tention a , and N can be calculateddirectly from the chromatogram asindicated in Figure 2 . In thi s figure,t , is the retention time of an inertsolute which is not retained by thestationary phase.Examination of Equation 4 showstha t t he resolution expression can bedivided into three parts: an efficiencyterm depending on L and H , a rateof migration term depending on k ,and a selectivity term depending ona .The selectivity term a dependssolely on the molecular forces be-tween the solute and th e two phases.Once the mobile phase, na ture of thestationary phase, and temperat ure arechosen, the relative retention is fixedand cannot be changed. As CY ap -proaches unity, th e resolution deter-iorates rapidly. The rat e of migration

    3Y , VOL. 46 , NO. 6 , MA Y 1974 511 A

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    Figure2. Calculation of some important parameters from chromatogram

    5 1 2 A * ANALYTICAL CHEMISTRY. VOL. 46 , NO. 6, M A Y 1974

    term depends on the intermolecularinteractions in the system, as well ason the amount of the sta tionary phase(or adsorbent surface area ). A s k ' in-creases for a given column system,the retention time also increases sothat a trade-off between the resolu-tion and analysis time must be made.Note th at increasing k' beyond acertain value (say 5) does not greatlyaffect the second term of Equation 4.If, however, k' is small, say 0.5-1,then increasing k' (to, say, the valueof 5)will increase markedly the resolu.tion. Lower k'values, although result-ing in shorter analysis time, are moredemanding in terms of-tbe efficiencyneeded for the resolution. As pre-viously mentioned, the resolution canbe improved by increasing the col-umn leng th. However, the retentiontime a nd the pressure drop across thecolumn are direct functions of thelength, whereas the resolution in-creases only with the square root ofthe length (Equation 4). Finally, im-proving the efficiency (Le., decreasingH)also improves the resolution. Im-proving the resolution by decreasingHis attractive since frequently it iseasier to manipulate the factors in-fluencing the plate height than otherfactors such as column length or na-ture of stationary phase.Now th at the importance of theplate height or column efficiency hasbeen demonstrated and th e relationbetween H nd the resolution estab-lished, we can proceed to discuss thevarious column processes th at hroad-en the solute zone.

    Chromatographic Efficiencyand Column Processes

    The d a t e height is a function ofthermddynamicand kinetic processeswhich take d a c e in the column. viz..molecular diffusion in th e mobilephase; mass-transfer phenomena inboth thesta tionaryand the mobilephases; an d flow irregularities.Theories such as the pla te model, therandom walk model, the nonequilihri-um model. and the mass balancemodel discuss these facton quantita -tivelv. The first three are discussedby Giddings ( 4 ) n his monograph,and the last is described adequatelyby Kucera ( 5 ) nd Grubner ( 6 ) oradsorption chromatography and byGrushka (7) for a partitioning system.This report does not attempt t o re-view these theories. Rather. we de-scribe rhe importance oi th e variouscontributors 10 rhe HETPa nd showbow they can he modified.Molecula r Diffusion. I:pon injcc-tion o i a mixture 01 ciht esin to rhechromau)graphir column. concentra-tion eradients w i r h resoect to the so -lutes exist simply because a t the mo-ment of injection the downstreamparts of the column do not containany of the solutes. According toFick's laws of diffusion, the solutezones will begin to broaden by diffu-sion in the axial direction. In liquidchromatography, because of the lowdiffusion coefficient value in the l iq-uid mobile phase (about 10W5 ma lsec), this broadening mechanism is

    usually not of practical importance(unlike GC a t low carrier velocities).Mass Trans fer. Mass transfer is aphenomenon which takes into ac-count the transfer of solute moleculesfrom one region in the chromato-graphic column to ano ther, and inchromatography the important pa-rameter is the ra te of mass transfer.Mass-transfer rate is important in thestationary phase, in stagnant pocketsofthe mobile phase (these pocketsare found in the pores of the supportparticles), and in the mobile phase.fer in the stationary phase meanslonger time spent in th e phase. Forexample, in liquid chromatographywhile some solute molecules are dif-fusing into and then out ofthe sta-tionary phase, others are moving withthe mobile phase. The result is abroadened zone. The ra te of masstransfer in this instance can be im-proved by reducing the film thicknessof the stationary phase and so reduc-ing the distance t ha t a molecule solutemust diffuse. Solutes will have highmass-transfer rates when their diffu-sion coefficients in the stationaryphase are high, bu t for a given LCsystem a t a given temperature, this isa variable beyond the control of theuser. Obviously, the mass transfer inthe sta tionary phase is a function ofthe parti tion coefficient (or the capac-ity ratio) since it indicates the affinityofthe solute to th at phase.Mass Transfer in Stagnant PocketsofMobile Phase. This factor can con-tribute significantly to H in LC (be-cause of the slow diffusion of the so-lute in it). In many respects, thi sphenomenon is similar to mass trans-fer in the stationary phase. The onlymechanism by which the solute mole-cules can leave a stagnant pocket isby diffusion through the mobilephase. Hence, for fas t mass transfer,the diffusion coefficient should hehigh and th e depths of the poressmall. This explains the successofpellicular packings, in which a porouslayer is bonded to a hard core, and ofporous microspheres. In these cases,the pores are shallow dr smal l, result-ing in good mass-transfer propertiesin the stagnant pockets and corre-spondingly high efficiency.However, recent work by Done etal . (8)ndicates tha t not all pellicularsupports are equivalent in their be-havior with respect to stagnant pock-et mass transfer. They also indicatetha t the dependence of Hon k' is afunction of whether the impor tantcontribution to the mass transfer isfrom th at in the stationary phase orthe stagnant mobile phase. In thefirst case (and only if it is the majorcontributor to the efficiency), theHETPwill have a maximum a t h' =1. n th e second case, H will keep in-

    Stationary Phase. Slow mass trans-

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    creasing with the capacity ratio. Ex-perimentally then, one can check thevalue of H a t a given mobile phasevelocity asa function of k and getsome insight as o the major contri-hution to the HETP. The disadvan-tage of pellicular packings will bementioned later.Mass Transfer in Moving MobilePhase. This is a complicated phe-nomenon. In a packed column, thevelocity of th e mobile phase is differ-eut from point to point owing to theperturbation caused by the supportparticles. Streamlines near the parti-

    lute molecules are diffusing in themobile phase continuously. Thus, atone moment a molecule can he in amobile phase st reamline whose pa this around a support particle. T he nextmoment, the solute molecule can dif-fuse laterally to a different streamlinewhose velocity is different and whosepath is relatively free (at least for ashort distance) of obstruction by thepacking.Hence, the tor tuous path of solutemolecules is due both to diffusingfrom streamline to streamline and tohaving to circumvent support parti -

    center or maximum). The faster therate of mass transfer, the closer thesystem would he to equilibrium.These points indicate th at a t high ve-locity and slow mass-transfer rates,the column efficiency would he lowerthan a t low velocity, all other condi-tions being equal. T o express it in ex-tremely simplified fashion, at highvelocity the rate of mass transfer isnot fast enough to catch up with theconstantly changing solute concentra-tion and the zone isbroadened.mobile phase, t he mass-transferA t extremely low velocity of thecle boundaries moye slowly, andstreamlines near the center betweenparticles move relatively more rapid-ly. In addition, some regions in thecolumn are packed more tight ly thanothers, again resulting in flow in-equalities (4).Some solute moleculescan be in slow streamlines, whereasothers move with faster velocities,

    thus broadening the zone.come this phenomenon is the diffu-sion of the solute molecules from onestreamline to another. In this man-ner, if the diffusion is fast enough,the solute molecules in the mobile

    The only mechanism th at can over-

    cles. This simultaneous dua l broad-ening mechanism is known as thecoupling effect (molecular diffusionis coupled with uneven pathlines)first discussed by Giddings ( 4 ) .Thecoupling effect manifests itself in giv-ing the H vs . mobile phase velocityplot its usual convex shape in LC. Itstands to reason that this goingaround the partic le broadeningmechanism is support size dependentand decreasing it should improve theefficiency.Effect of Mobile Phase Velocity.The mobile phase velocity affects theplate height since it determines the

    terms are less important, h ut broad-ening owing to molecular diffusionmight adversely affect H. In normaluse, however, the velocity is such (be-tween 0.1 to 10cm/sec) th at molecu-lar diffusion is negligible, and an Hvs. Uplot typically looks like the oneshown in Figure 3.Some workers in the field prefer touse reduced plate height h (defined asH divided by the size of the supportparticle) and reduced velocity Y (de-fined as the velocity multiplied bythe support size and divided by thediffusion coefficient of the solute inthe mobile ohase). These are ex-phase \?ill S(,L all rh e \urious flowraws and wil l move wirh the sampa\eraped o r i r ? . Thereiorc, tht: d i f fu -sion in the inoliile phase is an impor-

    re la t iw importanct. of the rcsi;tancero mass-triinirer rerms. The soluremolerulcs would like 10 distributeI hemselves h t a e e n the mobile and

    tremrlg inipwtanr piram( ters sincerhey allou,th(.cornparisonotcolumn~\r,ith dirierent packing sizvs and 1110-hile phases. Hrnrcv( r . owing to thetant parameter in determining the ef-ficiency. Since the maldist rihution inthe velocity of the carrier is due tothe packing particles, it makes senseth at t he solute molecules should dif-fuse a distance which isproportionalto the particle diameter in order tomove from one streamline to another,The smaller the particle, the fasterthe exchange between the various ve-locities in the column and the moreefficient the system. This is anotherreason for using smaller size supportparticles highapeed LC. Recently, forexample, Kirkland (9, O) and Majors(22, 221, among others, reported theuse of extremely small particles (lessthan 10 wm) which gave efficient col-umns. Majors shows the improvementin the efficiency and resolution ofseveral azo dyes th at can be obtainedin going from 13.2 fim average parti -clesizeto6.1pm (11).Mass transfer in the mobile phasecan also he dependent on the par ti-tion coefficient. The nature of the de-pendence, however, is not known ex.actly; in fact, in many cases it maynot be significant.the velocity effects described above,there is also a distance effect. Duringthe t ime t ha t some solute moleculestravel around particles, other gostraight through and move furtherdown the column. This obviously alsobroadens the zone. Actually, the pic-ture is more complicated hecause so-

    Flow Irregular ities. In addition to

    stationary phase and reach a sta te ofthermodynamic equilibrium. The for-ward movement of the solute zoneowing to th e flow of the mobile phasedoes not allow this equilibration totake place except at one point, name-ly, the center of the zone (assuminglinear isotherm). Oneitherside of thezone center, however, the constantlychanging solute concentration (owingto mobile phase flow) keeps the sys-tem removed from equilibrium.Two points should he clear. Thefaster the flow rate is, the farther thesystem is removed from equilibrium(again with the exception ofthe zone

    Figure 3. Typical HETP vs . mobilephase velocity curve in HSLC

    nature of this report, hand; will nothe discussed here and the interestedreader should consult ref. 8 (or 29 andreferences therein) .Additional Factors AffectingEfficiency and Resolution

    A solute zone may, owing to injec-tion of too large a mass or to injectionof an overly large sample volume,broaden symmetrically and yield anelution peak of greater H value thanthe intrinsic capability of the column.A frequent question in this connec-tion is whether a small hut concen-trated or a larger bu t dilute samplevolume should he injected. A recentstudy by DeStefano and Beachell (13 )shows that , at least for large-diametercolumns (10.8mm i.d.) and porousparticles, it is more advantageous tointroduce a large diluted volume oversmall bu t concentrated ones. Thisprocedure, according to them, over-comes the problem of locally over-loading the column a t the inlet withthe solutes. Kirkland, on the otherhand, shows (14) that in the case ofporous silica microspheres, increasingthe sample volume can increaseunduly the peak width of early elut-ing solutes (Le., solutes having smallpartit ion coefficients). This increasein the peak width was attributed toextra column effects such as connect-ing tubes and detector cell volume.Thus, one must be careful not to in-ject such a large volume as to in-5 1 4 A * ANALYTICAL CHEMISTRY, VOL. 46, NO. 6, M A Y 1974

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    Chemistry ofW inema kingADVANCES IN CHEMISTRYSERIES No . 137A. Dinsmoor Webb, Edito r

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    crease the width of early eluting so-lutes over and above the width th atresults from the usual processes inthe column.the linear capacity of the systemwhich is described as the weight ofthe sample per gram of packingwhich causes a 10%reduction in thespecific retention volume relative tothe cons tant retention volume oh-served for smaller samples . If con-stant injection volume is used, it isadvisable to operate a t sampleweights which are lower than the lin-ear capacity, since this will ensurebetter efficiencies. The linear capaci-ty of a chromatographic system canbe obtained by experimentation ( 2 4 ) .Ingeneral, however, as the surfacearea of the support increases, largersample injections can be made.It is also possible tha t parti tioncoefficients can he solute concentra-tion dependent , giving rise to asymimetrically shaped elution peaks.When the peaks tail (Figure 4, A),the position of the peak maxima de-creases with increased solute concen-tration; when the peaks front (Figure4, B), the peak maxima increase withincreased solute concentra tion. Inboth bases the asymmetry results in apeak broadening which reduces theresolution between peaks.It is thus desired a t times to runthe experiment with several differentsolute concentrations t o see whetheror not the peak width, peak asymme-try, and retention time are constant.Summary

    Th e efficiencyH , then , is a func-tion of the mobile phase velocity, th esolutes partition coefficient (or th ecapacity ratio), the diffusion coeffi-cient of the solute in the stationaryand mobile phases, the support part i-cle size and nature , the amount ofstationary phase on the support (filmthickness), and the surface area ofthe support in adsorption chromatog-raphy.To lower H and increase th e resolu-tion, several courses of action areavailable. Th e following is only arough guideline to some of the ap-proaches the investigator can take. [Amuch more comprehensive and sys-tematic discussion of improving theresolution in high-speed LC was re-cently given by Snyder (26, 2711.Decrease the carrier velocity.This, however, means longer analysistime. Also, one can increase the mo-bile phase velocity provided th at thecolumn length is increased propor-tionately.0 Decrease amount of stationaryphase in liquid-liquid system (but notto the point where adsorption on thenaked support begins to adversely af-fect H ) .

    Snyder (25)defined a term called

    Figure 4. Peak asymmetryA TailingB Fronfing

    Decrease the size of th e supportparticle. It must he emphasized hereth at when using small particles (Le.,less than 20 pm), packing becomes aproblem and special care must he ex-ercised when filling the column. Thispoint will he discussed shortly.Use a mobile phase having lowviscosity so th at the diffusion ofso-lutes in it is rapid. Also, for a desiredmobile phase velocity, lower viscositymeans lower inle t pressures.Lower the viscosity of the mobilephase by increasing the temperature .However, the effect of temperature onthe plat e height is less clear cut .Schmit et a l. (18) ndicated the Himproves with increasing tempera-ture, whereas Knox and Vasvari (19)found no dependence of H on thetemperature. An increase in the tem-perature results in a decrease ofh (orthe retention time) and most fre-quently in a. Th at decrease in LC ismost often more pronounced than anyimprovement in H, and the resolutioncan deteriorate with inkeas ing tem-perature (Equation 4) :Use a support where the likeli-hood of large stagnant pockets of mo-bile phase are minimized (pellicularpacking or microspheres with smallpores).HETP can he decreased by decreas-ing the size of the packing. H variesroughly as the particle diameter tothe power of about 1.8.As the part i-clesize decreases, the permeability ofthe column decreases, and higherinlet pressures are needed to drivethe mobile phase. The permeability isroughly a function of the square ofthe particle diameter. However, be-cause of the higher efficiency of the

    As mentioned previously, the

    516A ANALYTICAL CHEMISTRY, VOL. 46. NO. 6. M AY 1974

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    system, the column length can he de-creased, thus decreasing the neededpressure drop. Particles smaller than20 fim are more diff icult to pack uni-formly, and special techniques suchas balanced density slurry (20)areneeded. However, with care, particlesdown to 20 fim can he dry packed togive efficient columns ( 8 ) .Recentwork also shows that the shape ofsmall particles need not be sphericalfor efficient packing.Smal l porous particles have onedistinct advantage over pellicularpackings. The lat ter packing usuallygives short retention times and low-capacity ratiio value. It is, therefore,easy to overload the pell icular pack-ings. In addition, their price is ratherhigh. Porous supports, on the otherhand, are usually much less expensiveand, owing to their large surface area,can handle larger charges of solute in-jections.

    References

    (3 ) N . Hadden et al., "Basic Liquid Chro-matography,'' Varian Aerograph, 1971.(4 ) J. C . Giddings, "Dynamics of Chroma-tography," Marcel Dekker, New York,N.Y. , 1965.(5) E. Kucera, J . Chromatogr., 19,237119fiS)- - - ~ , .(6 ) 0.Grubner, n "Advances in Chrama-tagraphy," J. C. Giddings and R. A.Keller, Eds.,Vol6, p 173, Marcel Dek-ker, New York, N.Y. , 1966.(7!,Eirwhka, J . Phys. Chem . , 76,2586,'"l IA,.(8) J. N. Done, G. J. Kennedy, and J. H.Knax, "Gas Chromatography-1972," S .G. Perry and E. R . Adlard, Eds., p 145,Applied Sciences, Essex, England, 1973.(9) J. J. Kirkland,J . Chromatogr. Sci.,10, t(10) J

    (12) R. E. Majors and F. R. MacDonald,J . Chromatogr., 83,169 (1973).(13) J . J . DeStefana and H. C. Beachell,J . Chromatogr. S+, 10,654 (1972).(14) J. J. Kirkland in "Gas Chromatogra-phy-1972," S. G. Perry and E. R. Ad-lard, Eds., p 39, Applied Science, Essex,Fnrrlanrl 1471_ _ ~-..(15) L. R. Snyder,Anal.Chem . , 39,398

    '(16) L. R , Snyder,J . Chromatogr. Sei.,(1967).i n i nn i i q 7m_",-I" 1-" .-,.(17) L. R. Snyder, ibid.,p 369.(18) J.A. Schmit, R . A. Henry,R. C. Wil-liams, and J. F. Diechman,ibid.,9,64511971)_ " . - , .(19) J. H. Knox and G. Vasvari,J. Chro-(20) R. E. Majors,Anol.Chem. , 44, 1722motogr., 63,181 (1973).(1972).

    EliGrushka is ass istant professor ofchemistry a t the Sta te University ofNew York at Buffalo. His BS was ob-tained in 1963from Long Island Uni-versity, and his PhD from CornellUniversity in 1968.He did postdoctoralwork with Professor Giddings at theUniversity of Utah (1967-1QfiQ) T h(;nshk;l', research inrererhe arra of chromatograpt

    man;-La Roche In(

    ;tsare iniic theories,.--"- h:n-noenhancement of chromato,La,...Lolution, the utilization (phases and of liquid cry:matography, and in me;cochemical constants h:graphy. He has numeralpapers in the field of seFGrushka is a member ofand t he Chromatographic DiscussionGrouD. His current address is Hoff-:., Nutley, N.J.

    If bonded3tals in chro-rsuring physi-i chromato-JS scientificiaration. Dr .ACS, M A S ,

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