field flow fractionation in analysis of polymers and rubbers

Field Flow Fractionation in Analysis of Polymers and Rubbers

S. Kim Ratanathanawongs Williams and Maria-Anna Benincasa

inEncyclopedia of Analytical Chemistry

R.A. Meyers (Ed.)pp. 7582–7608

John Wiley & Sons Ltd, Chichester, 2000

FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS 1

Field Flow Fractionation inAnalysis of Polymers andRubbers

S. Kim Ratanathanawongs WilliamsColorado School of Mines, Golden,USA

Maria-Anna BenincasaUniversita di Roma, Rome, Italy

1 Introduction 1

2 Theory 22.1 Basic Theory of Retention 32.2 Molecular Weight Dependence on

Physicochemical Parameters 52.3 Conversion of a Fractogram to

Molecular Weight Distribution 62.4 Calibration Methods 62.5 Zone Broadening 72.6 General Theory of Asymmetric

Flow Field-flow Fractionation 82.7 Retention in Hollow-fiber Channels 9

3 Instrumentation 93.1 Flow Field-flow Fractionation 93.2 Thermal Field-flow Fractionation 103.3 Detectors 10

4 Experimental Procedures 114.1 Sample Preparation and Handling 114.2 Sample Injection and Relaxation 124.3 Operation with Constant or Pro-

grammed Field 13

5 Applications 135.1 Organic-soluble Polymers 135.2 Water-soluble Polymers 16

6 Method Development 176.1 Determining Experimental

Conditions 176.2 Effect of Sample Size 186.3 Membranes in Flow Field-flow

Fractionation 19

Acknowledgments 20

List of Symbols 20

Abbreviations and Acronyms 21

Related Article 21

References 21

Field-flow fractionation (FFF) was conceived by J. CalvinGiddings in 1966 as a separation and characterizationmethod for macromolecules, colloids, and particulates.Like chromatography, sample migration is caused bydifferential interaction with a field acting along an axisorthogonal to that of the transport liquid. Unlike chro-matography, where separation is achieved by solutespartitioning between mobile and stationary phases, sep-aration in FFF arises from the distribution of samplecomponents in fluid laminae flowing at different velocitiesin a single phase. The different flow velocities, described bya parabolic profile, arise from the high aspect ratio of theFFF channel. Different types of fields can be used in FFF aslong as they interact with some physicochemical propertyof the sample. The FFF channel design makes it highlysuited for analyses of fragile aggregates, high-molecular-weight polymers, and gels. In comparison with packedcolumns, shear rates in the channel and the probabilityof plugging the channel are low. The ability of thermalFFF to differentiate polymers and latexes of different bulkand surface composition is unique among currently usedseparation techniques. The FFF family of techniques canprovide a great deal of information about the sample butan initial time investment is often required for methodsdevelopment.

In this article, the fundamental mechanism of FFF isshown at play in the separation and characterization ofpolymers and rubbers by the two techniques par excellencein this field: flow FFF and thermal FFF.

1 INTRODUCTION

FFF is a separation method conceived by J. CalvinGiddings in 1966..1/ It is particularly suitable for macro-molecular, colloidal and diverse particulate materialsextending from a few hundred.2,3/ to 1018 Da..4/ It isan elution technique and is often referred to as achromatography-like technique. In chromatography, thesolute’s rate of migration is determined by its partitioningbetween a mobile phase and a stationary phase in a col-umn. In FFF, an externally applied field induces selectivedistribution of solutes in fluid laminae flowing at differentvelocities in a single phase inside a channel. The differencein the type of forces used in chromatography and in FFFdefines the range of applicability of the techniques. Whileforces in chromatography are localized at interfaces andvery selective, those used in FFF and electrophoresisare more diffuse and weaker. Consequently, the masstransport phenomena occurring in a chromatographictechnique, such as high-performance liquid chromatogra-phy (HPLC), tend to be slower as the solute molecularweight increases. When the molecule’s energy of inter-action with the interface is significantly greater than the

Encyclopedia of Analytical ChemistryR.A. Meyers (Ed.) Copyright John Wiley & Sons Ltd

2 POLYMERS AND RUBBERS

thermal energy kT, adsorption becomes irreversible..5/

However, even before irreversible adsorption appears,structural disruption and denaturation of the macro-molecular component may occur because of the strongshear forces present in the irregular flow in the tightlypacked chromatography column..6/ By contrast, the FFFseparation is carried out in the absence of a stationaryphase within an open channel. This channel is obtained byremoving a geometrical portion from a Teflon, Mylar, orpolyimide spacer and then clamping the spacer betweentwo flat parallel plates. As shown in Figure 1, the removedsection of the channel is a parallelepiped with taperedends that facilitate the flow of liquid and sample in andout of the channel. The most commonly used channeldimensions are 27–87 cm in length L, 1–2 cm in breadthb and 0.0075–0.05 cm in thickness w. Because of the veryhigh aspect ratio of the FFF channel and the frictionaldrag at the walls, the velocity of a liquid carrier movingin the longitudinal direction has a parabolic profile witha maximum in the center and minima, virtually zero, atthe walls. In the normal mode of operation, the fieldapplied perpendicular to the flow direction drives samplecomponents toward one wall, referred to as accumulationwall,.7/ with a velocity determined by the particle–fieldinteraction. This field-induced displacement, optimized inthe absence of longitudinal flow, is always counteractedby the diffusive flux that originates from the concen-tration gradient across the channel. The combination ofthese opposing effects results in a nonuniform distri-bution of components across the channel, those with ahigher rate of back-diffusion being driven further awayfrom the accumulation wall than those with a lower diffu-sion rate. Because of the parabolic flow velocity profile inthe channel, the faster-diffusing component C shown inFigure 1 will be displaced along the channel more rapidlythan component B, which has a lower diffusivity. Theoutput signal, collected by a detector sensitive to somesolute property, will thus register the elution profile ofdistinct peaks.

The normal mode of operation described above is theone mostly used for polymer separations because of themolecular size/weight range of these particular materials.Another retention mechanism, steric FFF,.8,9/ comes intoplay when the component size is significant relativelyto the channel thickness. This is generally the case forparticle dimensions higher than 1 µm. The solute elutionvelocity is determined, in this case, by the extensionof component particles into the flow. Larger particlesextend into regions of faster streamlines because of stericexclusion from the accumulation wall and elute earlierthan smaller particles. The retention order in this modeis reverse of that in the normal mode of operation.

Given the precise channel geometry and the flowprofile that may be described mathematically, retention

FFFchannel

A

B

B

C

D

C

Field

Field

Outflow

Inflowx

y

z

w

wb

Separatedbands

Parabolicflow profile

Figure 1 Schematic diagram of a typical FFF channel andthe normal mode FFF separation mechanism. (Reproducedfrom L.F. Kesner, J.C. Giddings, High Performance LiquidChromatography, eds. P.R. Brown, R.A. Hartwick, Chapter 15,1989. Copyright 1989, John Wiley & Sons, Inc. Reprinted bypermission of John Wiley & Sons, Inc.)

in FFF may be accurately calculated in theory and relatedto various solute physicochemical properties..10,11/ Theparticular sample property controlling retention dependson the type of the applied field. The use of differentfields has generated a number of FFF techniques, such assedimentation field-flow fractionation (SdFFF).12/ whena centrifugal force is used to induce retention, flow field-flow fractionation (FlFFF).13/ when the field is establishedby a transverse or crossflow of liquid, thermal field-flowfractionation (ThFFF).14/ when a thermal gradient is used,and electrical field-flow fractionation (ElFFF).15/ whena potential gradient is applied to electrically chargedsolutes.

FFF is particularly suitable for the separation of macro-molecular samples and suspended colloidal particles ofvarious origins because of the minimal surface area of thechannel compared with the total surface area of a packedchromatographic column (107 cm2)..16/ For this reason,adsorption phenomena are greatly reduced in FFF. Thedriving force may be accurately adjusted to yield thedesired levels of retention without the need to change thecolumn as in chromatography and sample distributionbetween zones is very fast because no phase boundariesmust be crossed. A rich literature is available for a greatnumber of applications from colloids of environmentalorigin.17/ to bacteria and viruses..18/

2 THEORY

The theory of retention discussed in this section isdeveloped for point particles at infinite dilution, that


is, for species with negligible size with respect to thechannel dimensions, particularly its thickness. When thisassumption is not satisfied corrections must be madeto account for the particle size. One such correction isconsidered in the retention model for steric FFF.

2.1 Basic Theory of Retention

Let us consider the space between two parallel platesand a field applied orthogonal to them in the x-direction (measured across the channel thickness fromthe accumulation wall). Under the effect of the field alone,component particles are displaced with a velocity U. Theparticles’ motions give rise to a field-induced flux Ucdefined as the number of particles per unit cross-sectionalarea per unit time directed toward the accumulationwall, that is in the negative x-direction. The field-induceddisplacement is, however, counteracted by a diffusive fluxproportional to the concentration gradient dc/dx throughthe component’s diffusion coefficient D and directed inthe positive x-axis direction. The mass transport across thechannel determines a net flux Jx given by Equation (1):

Jx D Uc�Ddcdx

.1/

The concentration profile across the channel thicknessreaches a steady state when the field-induced and diffusivefluxes are at equilibrium. At this point the net flux is equalto zero. Equation (1) is integrated and solved, assumingconstant U and D, to give an equation that describes thesteady state concentration profile (Equation 2):

c.x/c0D exp

(�jUj

Dx)

.2/

where c0 is the concentration at the accumulation wall,x is the distance from the wall, and jUj is negative forconsistency with the coordinate system. Concentrationdecreases exponentially from the accumulation wall.Since it may be shown that an exponential distributionbehaves as a much thinner layer positioned at acharacteristic height `, Equation (2) may be rewrittenas Equation (3):

c.x/c0D exp

(�x`

).3/

where (Equation 4)

` D DjUj .4/

The mean layer thickness ` is a measure of the averagedistance of a sample component from the accumulationwall. It is apparent from Equation (4) that ` depends onthe opposing effects of the field that acts to compress thesolute layer and the diffusion process that broadens it. The

quantity ` is frequently expressed in the dimensionlessform shown in Equation (5):

l D `

wD DjUjw .5/

where w is the channel thickness and l is the retentionparameter basic to FFF equations. Since l may beshown to be dependent on the field strength and on asample–field interaction constant, each component willhave a characteristic l value.

After the formation of the steady-state zone, a streamof liquid is allowed to flow along the longitudinal axisof the channel. Component particles are then carrieddownstream with an average velocity that depends on theregion where they are found. The sample distributionat this point assumes a Gaussian distribution in thelongitudinal direction because of the free diffusive motionof component molecules between regions of differentvelocities across the channel. The elution time will thenbe different for different components and may be usedto measure the sample elution velocity once the channelvoid volume is known. Elution time, however, is notthe most universal parameter defining the behavior of aspecies migrating along a chromatographic column or anFFF channel since it always depends on the average fluidvelocity. The dimensionless retention ratio R, defined asthe ratio of component migration velocity vp to the meanfluid velocity hvi (Equation 6),

R D vp

hvi .6/

is a more useful parameter. R is widely used in separationtechniques as a measure of the retardation of the soluterelative to the liquid carrier flow velocity. It is a moreuniversal measure of retention than elution time andonly depends on the field strength and on the particleproperty responding to the field, regardless of the flowvelocity. It then frees the mathematical architecture froma variable. In the expression of R, the solute meanmigration velocity is the average of the particle velocitiesexpressed as vp D hcvi/hci..19/ Inserting this expressioninto Equation (6), substituting the concentration termwith Equation (3) and the parabolic function to calculatev, and using Equation (5), one obtains an expression forR whose solution is given by Equation (7):

R D 6l(

cot h1

2l� 2l

).7/

Equation (7) is the basic retention equation in FFF. Itshows that retention is solely dependent on l, which ischaracteristic of each eluting species. Approximate formsof Equation (7) may be used for low l values or high levelsof retention. In particular, the approximation R D 6l has


an error of 20% at R D 0.25. The empirical relationshipR D 6.l� 2l2/ has the greater range of applicabilitywith less than 10% error up to R D 0.7. The retentionratio may also be written as R D t0/tr since V D L/tr andhvi D L/t0, where t0 is the residence time of the eluent orof a nonretained component and tr the average sampleresidence time or retention time.

In theory, any external field to which sample compo-nents are responsive may be used to induce selectiveretention and fractionation by FFF. The applied fielddetermines the type of interaction and hence the sampleproperty that will be measured. Besides FlFFF, ThFFF,SdFFF and ElFFF, the theoretical foundation has alsobeen laid down for many less developed FFF techniques.One such technique uses a concentration gradient in asolvent mixture to establish a chemical potential gradientcapable of driving solutes towards regions of lowest poten-tial [concentration field-flow fractionation (CFFF)]..20/ Anonuniform electric field that induces charge polarizationmay exert selective dielectrophoretic forces on compo-nent particles and generate fractionation..21/ Interestingapplications are reported using a magnetic field..22/ Pho-tophoretic FFF.23/ is based on the transfer of momentumfrom a photon to a particle. An acoustic wave field.24/ mayinduce retention selective to particle diameter in additionto other parameters.

The present discussion focuses on the FFF techniquesthat have been applied to polymer separations: FlFFFand ThFFF. These techniques have been extensively usedfor a great number of different samples. They are theFFF techniques par excellence for polymer fractionation.ElFFF has shown its potential only with a new channeldesign.25/ and may prove to be very useful for thecharacterization of charged polymers.

In his investigations on the theory of Brownian motion,Einstein.26/ showed that in a system of point particles atinfinite dilution, i.e. in the absence of flow perturbationsdue to the motion of one particle affecting another,the diffusion coefficient is inversely proportional to thefriction coefficient (Equation 8):

D D kTf

.8/

If D is replaced with the Einstein equation and therelationship for the field-induced velocity specific forFlFFF (U D PVc/Lb) is used in Equation (5) one obtains

l D kTf

V0

PVcw2.9/

In Equation (9), the relationship V0 D Lbw is also used toreplace Lb with V0/w. It is worth noting that Equation (9)depends on the friction coefficient f as well as on theinstrumental parameters V0 and w. This is not the case

with SdFFF where both D and U depend inverselyon f , which then cancels out in the ratio D/jUj. Thedependence of the retention parameters l and R on thefriction coefficient in FlFFF is the key to obtaining solutephysicochemical parameters from FFF measurements.More than a century before Einstein’s work in this area,Stokes.27,28/ found a quantitative relationship betweenthe shape and the dimensions of a moving particle andits friction coefficient. For a spherical body of radius R0

moving in a fluid of viscosity h he showed that the frictioncoefficient could be expressed by Equation (10):

f0 D 6phR0 .10/

Stokes’ equation may be used to relate diffusion coef-ficient to particle dimensions. Correction factors thatextend Stokes’ relation to nonspherical particles werefirst introduced by Perrin.29/ and Herzog et al..30/ forsolids of revolution such as prolate (cigar-shaped) andoblate (disk-shaped) ellipsoids. They chose to express thedeparture of the actual friction coefficient f , for an ellip-soid with axes of symmetry of different length from thefriction coefficient of a sphere of same volume f0. Theyfound a quantitative relation between f/f0 and the ratioa/b of the semimajor axis a to the semiminor axis b. Bycombining Equations (8) and (10), Equation (11):

D0 D kT6phR0

.11/

is obtained. The Stokes–Einstein relation in Equa-tion (11) is derived considering equivalent particle orien-tation which applies rigorously only to spherical bodies.The substitution of Equation (10) into Equation (9) givesthe expression for l in FlFFF (Equation 12):

l D kT6phR0

V0

PVcw2.12/

which shows explicitly the effective size-based separationin normal-mode FlFFF where samples are retainedproportionally to their hydrodynamic dimensions.

The expression for l in ThFFF is derived usinga conceptual procedure similar to that followed forFlFFF. The derivation of this expression is complicated,however, by the distortion of the parabolic flow profiledue to changes of viscosity with temperature across thechannel..31,32/ In 1856, Fick (and later Soret in 1859)showed that if a salt solution of uniform concentrationin a tall container is heated at the top and cooled at thebottom, a flux of matter originates that increases the saltconcentration at the cold end of the column. This effect,named after Soret, is known as thermal diffusion since itis clearly a diffusive effect occurring only in the presenceof a thermal gradient. The equation of flux (Equation 1)


set for molar thermal and diffusive fluxes gives

Jx D �D(

dcdxC cg

dTdx

)�DTc

dTdx

.13/

where DT is the thermal diffusion coefficient and g is thecoefficient of thermal expansion. The solution for zeronet flux at the steady state yields the retention parameterfor ThFFF (Equation 14):

l D[

w( a

TC g) dT

dx

]�1

.14/

wherea is the thermal diffusion factor equal to DTT/D..33/

Both a and dT/dx depend on the local position x and thuson the temperature. The ordinary diffusion coefficientis strongly dependent on the temperature through theT/h term in Equation (11) where 1/h also increaseswith T. In the case of flexible-chain macromolecules,it must be borne in mind that, on polymer chemistrytheoretical grounds, the molecular coil is expected toexpand on increasing temperature as a consequence ofthe increased excluded volume. This property is treatedin terms of the second virial coefficient..34/ The tendencyof polymer hydrodynamic dimensions to increase withtemperature is reported in light-scattering studies..35/ Thelocal temperature gradient is not independent of T.31,32/

but the dependence is relatively small. DT is shown todepend on temperature.36/ but to a smaller extent thanthe ordinary diffusion coefficient. In the standard theoryof FFF, however, l is generally used in an approximateform that is valid at high retention where the samplecloud is very close to the accumulation wall. The localvalues of dT/dx and a may therefore be assumed to bethe same as those at the cold wall..37/ The term g becomesnegligible.31/ and l may be rewritten as in Equation (15):

l ³ Tc

aw(

dTdx

)c

D D

DTw(

dTdx

)c

.15/

where .dT/dx/c is the temperature gradient at the coldwall.

2.2 Molecular Weight Dependence on PhysicochemicalParameters

Synthetic polymers are often flexible-chain moleculeswhose dimensions cannot be defined precisely and mustbe considered as average values of all the configurationsthat the molecules assume. In such a situation it isconvenient to introduce a new parameter called the radiusof gyration, Rg. It is found from polymer theory thatmolecular weight may be related to polymer moleculardimensions through this statistical parameter according

to Equation (16):

R2g /

MM0

.16/

where M is the molecular weight and M0 is themolecular weight of the repeat unit (constant for synthetichomopolymers). The equivalent radius Re, defined as theradius of an equivalent sphere having the same value ofthe friction and diffusion coefficients as the polymer, isa convenient parameter that is often used. Since it maybe demonstrated that Rg / Re,.34,38/ equations dependenton Rg may be written in terms of the equivalent radius.For approximately spherical molecules, the volume of themolecule is linearly related to molecular weight. This maybe expressed as Equation (17):

R0 /M1/3 .17/

where R0 is the radius of a spherical particle. Globularproteins are an example of a real system that satisfiesthe model of a rigid spherical body. Even in such asimple case however, correction factors must be appliedto Equation (17) to account for the hydration volume anddeviation from the perfectly spherical symmetry. Whenthe polymer molecule is a statistical chain that is allowedto meander randomly in a Brownian-like way with noforbidden physical volume, polymer theory shows thathR2

gi is proportional to the number of repeat units inthe macromolecule chain given by N DM/M0. It followsthat the equivalent radius (or Stokes radius) is given byEquation (18):

Re /M1/2 .18/

If the polymer chain is not allowed to self-cross, thereis some space occupied by other polymer segments fromwhich each segment is excluded. Polymer conformationsare significantly affected by the excluded volume and theequivalent radius for a three-dimensional polymer chainmodel becomes (Equation 19):

Re / .M6/5/1/2 .19/

Based on the model of the equivalent sphere (Stokes–Einstein relationship), Equation (11) may be applied topolymers in solution, and the diffusion coefficient, at agiven temperature, may be related to molecular weightthrough the polymer equivalent dimensions Re and thefriction coefficient..38,39/ Substituting Equation (18) or(19) into Equation (11) and grouping together all theconstants, we obtain Equation (20):

D D AM�b .20/

where A is constant for a given polymer type and b is anexponent that depends on the polymer conformation in


solution. The value of the exponent in Equation (18)is obtained on theoretical grounds, considering zeroattractive or repulsive interactions between differentpolymer segments as well as between polymer moleculesand the surrounding medium. It also assumes infinitelydilute systems of neutral, nonfree draining moleculeswith average spherical symmetry. A system under theseconditions is defined as a -system (theta-system) at -temperature. -conditions are set by the type of solvent(which determines the energy of interaction with thepolymer molecules) and by the temperature. Generally,only one solvent behaves as a -solvent for a givenpolymer type. Therefore, the theoretical value of the bexponent is always related to a specific polymer–solventsystem at -temperature. The excluded volume has aconsiderable swelling effect on flexible-chain moleculesand on the dependence of particle size on molecularweight. The excluded volume effect is similar to andmay also be thought of as that due to a good solventor to a temperature higher than the -temperature. Byrelating the diffusion coefficient and molecular weight ata given temperature, Equation (20) allows FFF-measuredparameters to be correlated with the polymer molecularweight. Combining Equations (12) and (20), it appearsthat l in FlFFF is inversely dependent on molecularweight, that is, the zone mean migration layer decreasesas the polymer molecular weight increases (Equation 21):

l D AM�b V0

PVcw2.21/

A similar expression for ThFFF is complicated by the DT

term in Equation (15). In the classical theoretical treat-ment of FFF, DT is considered independent of molecularweight,.37/ as predicted and experimentally observed bysome authors.40/ (see section 5.1). Other authors,.41,42/

however, report a molecular weight dependence of thethermal diffusion coefficient. Assuming that, at a giventemperature, we have (Equation 22):

DT D BMb .22/

and considering Equation (20) for the dependence of theordinary diffusion coefficient on molecular weight, theoverall contribution of molecular weight to l in ThFFF isgiven by the D/DT term as Equation (23):

DDTD A

BM�.bCb/ D M�n .23/

where D A/B and n D bC b. The parameter mustbe temperature dependent because of the dependenceof D on temperature. Equation (23) substituted intoEquation (15) yields a negative exponential correlation

between l and the molecular weight (Equation 24):

l D M�n 1

w(

dTdx

)c

.24/

2.3 Conversion of a Fractogram to Molecular WeightDistribution

To obtain a meaningful molecular weight distributionof a polymer sample, it is necessary that elution occursin the same mode (normal, steric, etc.) over the entireretention time interval with a monotonic function of somesample property. Transformation of a fractogram froma time-based function to a molecular weight functionis readily accomplished but requires a correction tothe amplitude to account for the nonlinear relationshipbetween M and tr. The mass abundance in a timeinterval dtr, corresponding to c.tr/ PVdtr, must equal themass comprised in the corresponding molecular weightinterval dM. Integrating the mass distribution m(M) overthat interval yields Equation (25):

m.M/ dM D c.tr/ PVdtr .25/

where c(tr) is the detected sample concentration at timetr and PV is the volumetric channel flow rate. For dtr ! 0,Equation (25) becomes Equation (26):

m.M/ D c.tr/ PV dtrdM

.26/

The scale correction function dtr/dM allows the con-version of the retention timescale to the molecularweight scale. For a normal-mode elution, the molecu-lar weight distribution may be obtained in theory fromfirst principles..43/

2.4 Calibration Methods

It may be shown that the scale correction functiondepends on the constants A and b for FlFFF and and n for ThFFF, through the dependence of l onmolecular weight. These constants may be found fromtheory and are available in literature for a wide numberof polymer–solvent systems. However, it is commonlaboratory practice to obtain them through a calibrationprocedure with a set of well-characterized, narrowlydistributed polymer standards whose molecular weightshave been measured by some absolute technique such aslight scattering, viscometry or osmometry. To obtain Aand b values that can be transferred to an unknownpolymer sample, calibration must be performed withstandards of the same or similar composition as theunknown, in the same carrier liquid and at the sametemperature. Constants A and b for the FlFFF analysis of


polymers are obtained from the intercept and slope of aplot of the measured log D versus log M (Equation 27):

log D D log A� b log M .27/

derived from Equation (20). The plot of log l versus logM would also give these constants. A similar log lTversus log M plot provides the constants and n for thecalibration in ThFFF. Gao and Chen.44/ and Giddings.45/

have shown the system transferability of the ThFFFcalibration constants. A more detailed treatment of the‘‘universal calibration’’ in ThFFF.46/ also accounts forthe change of the cold wall temperature on polymerretention and on the calibration constants. FFF constantsallow a more universal calibration than size-exclusionchromatography (SEC) since they are derived fromfundamental physical properties of the carrier liquid andof the polymer under investigation and do not dependon any system parameter. In contrast, calibration in SEChas no rigorous theoretical grounds; it is not valid forsome pore structures.47/ and it is therefore not systemtransferable. Moreover, it is still under evaluation forsome types of polymers.48 – 50/ and does not always applyto different polymer samples.51,52/ even when run in thesame column under the same conditions..16/ Calibrationin FFF may also be performed using a set of polydispersestandards.53,54/ or with a single broadly disperse samplewhen the relative molar mass is measured at two or moreretention times by an absolute technique such as lightscattering.55/ or mass spectrometry..56/ It should be notedthat absolute molecular weight (M) measurements madeby FlFFF combined with mass spectrometry show anexcellent data fit for log l (and thus D) versus log M atmolecular weight values far lower than those predictedfrom polymer theory.

2.5 Zone Broadening

The previous discussion on calibration in FFF assumedthat broadening of the peak was due solely to molecularmass differences. In contrast, a number of concomitanteffects contribute to the increase in peak width. Ameasure of zone spreading, and hence of resolution,is given by the plate height. As with other separativetechniques, the overall plate height in FFF is given by thesum of contributing uncorrelated terms (Equation 28):

H D Hl CHn CHr CHp C∑

Hi .28/

In Equation (28), the zone spreading due to longitudinaldiffusion Hl arises from concentration gradients alongthe sample plug and increases with the residence time.It is linearly related to the diffusion coefficient asHl D 2D/Rhvi and therefore becomes negligible for veryslowly diffusing components such as macromolecules. In

contrast, the nonequilibrium term Hn arising from therandom displacement of component molecules across thechannel is one of the dominant contributions to peakbroadening in FFF. The band spreading associated withthe time needed for the zone to reach the equilibriumposition in the presence of the longitudinal flow, Hr,may be minimized by adopting a stop-flow procedure(see later). Other contributions,

∑Hi, associated with

system nonidealities such as dead volumes or injectionvolumes, may be disregarded in a well-designed channel.The spreading due to differences in a characteristicproperty such as molecular weight Hp is only an apparentbroadening. It arises from the fact that individualmolecules of a macromolecular or a particulate samplemay differ somewhat from one another in their relativemass or size and are retained to a slightly differentextent. If the difference in M is not large enough toproduce distinct peaks, the sample zone will appearas a broadened peak with different mass elementscontinuously distributed in a molecular weight interval.It may be shown that (Equation 29):.57/

Hp D LS2M.µ� 1/ .29/

where µ DMW/MN is the sample polydispersity indexwhich gives a measure of the departure of the weight-average molecular weight MW from the number-averagemolecular weight MN. For monodisperse samples, the twoaverages coincide. It appears from Equation (29) that theplate height, and hence resolution, strongly depend on thesystem selectivity SM, which is defined as the retentionvolume difference of components of different M relativeto the molecular weight difference (Equation 30):.58/

SM D∣∣∣∣d ln Vr

d ln M

∣∣∣∣ D ∣∣∣∣ d ln Rd ln M

∣∣∣∣ .30/

The subscript M denotes a molar mass-based selectivitywhose value is a measure of the system ability todiscriminate samples by their mass. Under conditionsof high retention, the approximation R D 6l may be usedand SM becomes in the limiting form (Equation 31):

SM D∣∣∣∣ d ln l

d ln M

∣∣∣∣ .31/

Application of Equation (31) to Equations (21) and(24) shows that selectivity values for FlFFF and ThFFFcoincide with the exponent of molecular weight, i.e. bin FlFFF and n in ThFFF. Assuming that the thermaldiffusion is independent of molecular weight, b andn may be associated with the polymer molecule con-formation in a given solvent and temperature system.From polymer theory, values of exponent b are pre-dicted to be 0.33 for solid spheres, 0.5 for random-coilmacromolecules.39/ in -conditions and about 0.7 for


flexible-chain polyelectrolytes..59/ The theoretical selec-tivity for FFF is considerably higher (0.5–0.7).60/ thanthat for SEC, where typical values range between 0.05and 0.1..58,61/ Differences in selectivity when polymersare analyzed in organic solvents or aqueous solutionsare expected considering that water generally behavesas a good solvent for hydrophilic polymers whereas-systems are mostly reported for neutral polymers inorganic solvents. The theoretical value of 0.588.38,62/ forpolystyrene (PS) in tetrahydrofuran is obtained in ThFFFat a specific cold wall temperature..46/ The same poly-mer, run in ethylbenzene by FlFFF,.63/ gives a selectivityranging between 0.51 and 0.56. Synthetic water-solublepolymers are generally fractionated with a selectivityabove 0.6..64 – 69/ Polyvinylpyridine is an interesting exam-ple of a polymer that behaves as a neutral statisticalchain in tetrahydrofuran and as a charged coil in waterwhere it is soluble only as a polyelectrolyte. This poly-mer, bearing a six-term aromatic ring in the repeat unit,is fractionated with a selectivity of 0.51 in tetrahydro-furan by ThFFF and of 0.62 in an aqueous medium atlow pH..65/ Systematic studies of polyelectrolytes in aque-ous solution by FlFFF indicate a strong effect of thesolution ionic strength on the selectivity, which gen-erally decreases with increasing concentration of theadded simple electrolyte..68/ Further investigations onthe change in selectivity with the ionic strength of aque-ous solutions and with the type of added electrolytehave been used to show specific interactions between thepolymer and some metal ions..69/ Retention and selec-tivity in ThFFF of neutral polymers in organic solventsappear to increase with rising solubility parameters ofthe polymer–solvent system..70/ This effect was first reg-istered in early investigations on ThFFF of polymers..37/

Comparative studies on the separation of copolymersby ThFFF and gel permeation chromatography (GPC)show that only the former yields a good separation ofa diblock copolymer of poly(styrene-co-isoprene) froma triblock poly(styrene-co-isoprene-co-styrene)..71/ ThisThFFF separation is attributed to the difference in ther-mal diffusion coefficient of the two polymers.

2.6 General Theory of Asymmetric Flow Field-flowFractionation

The general concepts of FFF were first developed foruniform field strengths and constant flow velocities alongthe channel. The symmetric FlFFF channel, shown inFigure 2(a), was designed to achieve these characteristics.In 1987, Wahlund and Giddings.72/ introduced a newdesign of a FlFFF channel with only one permeable walland no independent transverse flow. In this variant ofFlFFF named ‘‘asymmetric FlFFF’’, shown in Figure 2(b),the permeable upper wall is replaced by a solid glass

Permeable frit

Membrane

Permeable frit

Crossflow in

Crossflow out

Symmetric flow FFF

(a)

Glasswall

Membrane

Permeable frit

Crossflow out

Asymmetric flow FFF

(b)

Hollow-fibermembrane

walls

Crossflow out

Crossflow out

Hollow-fiber flow FFF

(c)

Figure 2 Different configurations of FlFFF channels. Thesymmetrical (a) and asymmetric (b) channels are commerciallyavailable and thus more commonly used than the hollow-fiberconfiguration shown in (c).

plate that conveniently allows visual inspection of theinterior of the channel. Both the channel and crossfloworiginate at the channel inlet but exit the channelas two separate streams at the channel and crossflowoutlets. Using this asymmetric channel configuration,a crossflow velocity gradient is established across thechannel thickness. The sample concentration in thetransverse coordinate in this design may no longerbe described by Equation (3), but it approaches theexponential distribution of the standard FFF model forhighly retained samples. Expressions for R and l arefound following the same mathematical procedure asin the symmetric configuration but taking into accountthat the flow velocity profile is linearly decreasing alongthe channel at a rate determined by the crossflowvelocity. For high retention levels (x/w ³ 0.1), l mayagain be approximated by Equation (9). Rectangularand trapezoidal.73/ shaped channels have been usedin asymmetric FlFFF. In the latter case, the breadthdecreases as a function of channel length. An exponential


decrement in channel breadth.74/ is shown to give aconstant average channel flow velocity.

2.7 Retention in Hollow-fiber Channels

An interesting but commercially unavailable configura-tion of FlFFF utilizes a hollow cylindrical fiber withporous walls in place of the rectangular channel..75/ Inthis arrangement, illustrated in Figure 2(c), the axial flowis provided by an external pump connected with the inletof the hollow-fiber membrane while the transverse flowis obtained by removing liquid radially from the channelwith a second pump. The two flow velocity profiles inthis configuration are different from any of the previ-ously described FlFFF systems, both being variable withthe distance Z from the inlet because of the pressuredrop along the channel. From studies of fluid dynamicsin hollow fibers,.76/ it is found that the axial and radialflow velocities decrease exponentially as a function of Zand the permeability of the fiber and the fluid viscosity.Retention time in this type of channel is a function ofchannel length and Peclet number.

3 INSTRUMENTATION

An FFF system is generally assembled in a manner similarto that of a chromatographic apparatus. It uses most of theancillary equipment employed in chromatography suchas injector valves, pumps for the carrier liquid delivery,detectors, and some data acquisition devices such as chartrecorders or more conveniently computers. A generalizedFFF system is shown in Figure 3.

3.1 Flow Field-flow Fractionation

FlFFF is the most universally applicable FFF techniquebecause any solute particle is subject to transport in aliquid stream. As shown in Figure 4, the spacer contain-ing the channel form is clamped between two parallelblocks of some material such as Plexiglas, polyethylene,

anodized aluminum, or stainless steel that accommodatetwo porous frit panels with 2–5-µm pores. Ceramicfrits are more commonly used while polyethylene,.64,77/

polypropylene,.18,78/ and stainless steel.63,64,79/ are gener-ally employed with clamping blocks of the same material.An important component of the FlFFF channel is a per-meable, generally polymeric, membrane placed over theaccumulation wall to impede sample loss through the frit.Given the importance of the membrane in the success-ful application of FlFFF, a specific section (section 6.3)is dedicated to this topic. The design of the asymmetricFlFFF channel is somewhat different from that of thesymmetric channel, as shown in Figure 2(b), but besidesthe dissimilarity of the channel geometry and the absenceof the top porous wall it bears few differences from thesymmetric FlFFF system. Some operational procedures,such as sample injection and relaxation, however, differfrom those routinely used in the symmetric channel. Ahollow-fiber channel has to be placed in a mantle, possiblyof cylindrical symmetry, such as an empty stainless-steel chromatographic column, and the two coaxial tubessealed to each other at the ends. The mantle must have aport connected to a crossflow pump that draws fluid outthrough the wall of the fiber. The channel flow is suppliedby another pump connected to one of the hollow-fiberextremities. Sample injection and relaxation also in thiscase are particular to the set-up and will be dealt with insection 4.2.

Standard FFF theory assumes constant and uniformfield strength and average flow velocity in the length andbreadth dimension (edge effects not considered). There-fore, accurate control and continuous measurements ofboth these parameters are necessary when operating anFFF system. In FlFFF, the pump flow rates for boththe longitudinal and transverse streams must be keptconstant and continuously checked because, after mix-ing inside the channel, both flows may exit the channelthrough the outlet with the lower pressure. It is there-fore of primary importance to equalize the pressures atthe channel and crossflow outlets. This is achieved byplacing back-pressure regulators at one or both outlets

Pump

Carrierreservoir

Injectionvalve

Field

Channel

Detector

ControlComputer

Data acquisitionFlow rate

measurement

Fractioncollector

Waste

Figure 3 FFF system assembled with the ancillary equipment.


��

��

Channel flow in (sample injection)

Channel flow out(to detector)Crossflow in

Clampingblock

Porous frit

Spacer

MembranePorous frit

Clampingblock

Crossflow out

FFF channel

Figure 4 Diagram of the constituent elements of a FlFFF channel. (Reprinted from M.H. Moon, J.C. Giddings, J. Pharm. Biomed.Anal., 11, 911–920 (1993). Copyright 1993, with permission from Elsevier Science.)

and checking the pressure with in-line pressure gauges.An easy, cheap, but time-consuming method to check theflow rates is to measure the liquid volumes displaced overunit time with a buret and a stopwatch. Alternatively, abalance can be used to measure the weight of the car-rier liquid exiting from each outlet as a function of time.The balance may be connected to a computer.80/ to storedata on time-dependent flow rates that may be used foraccurate calculations of the retention parameters. This isparticularly useful in programmed runs (see later) wherethe field strength, and hence the crossflow rate, is variedwith some function of time.

3.2 Thermal Field-flow Fractionation

ThFFF channels (Figure 5) are formed by clamping apolyimide spacer (with the FFF channel volume removed)between two copper blocks with highly polished nickelor chromium surfaces. The field in this system is athermal gradient that is provided by electrically heatedmetal elements inserted into one block and a streamof cold water flowing through the second block. Holesare drilled into the copper blocks to allow the insertionof temperature-measuring probes at different positionsalong the channel.

3.3 Detectors

Virtually any of the detectors used in chromatography iscompatible with FFF apparatus. The HPLC separation

��

yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Coolant circulationCold copper barSpacerCartridge heater

Hot copper bar

Channel inlet Channel outlet

Figure 5 ThFFF channel. (Reprinted with permission fromJ.C. Giddings, V. Kumar, P.S. Williams, M.N. Myers, Adv.Chem. Ser., 227, 3–21 (1990). Copyright 1990, American Chem-ical Society.)

mechanism generally induces a concentration of theinitial sample plug so that samples of continuouslydecreasing concentration may be detected. In FFF,the solute plug undergoes considerable concentrationduring the relaxation process.81/ and considerable dilutionduring separation and elution. While reduction of theinjected sample mass is always sought, particularlyfor high-molecular-weight polymer samples, the finalconcentration must be considered and the injected loadadjusted to give a good signal-to-noise ratio. Nonspecificdetection methods, such as refractive index.61,71,82,83/ orviscosity,.84/ may be generally used while others maybe employed only when the solute is susceptible tospecific response. This is the case for spectrophotometricdetection, one of the most widely used methods inchromatography and FFF. Spectrophotometric detection


0.7105

106

0.8 0.9 1.0 1.1 1.2

M

Ve (mL)(a)

(b)

1.0

0.8

0.6

0.4

0.2

0.0105 106

MW

dW/d

M

(c)105 106

M

100.0

10.0

1.0

Rg

(nm

)

Figure 6 ThFFF/MALS of PS microgel. (a) Increase in molec-ular weight with increasing elution volume Ve; (b) molecularweight distribution determined from MALS (dashes) and cal-culated by calibration (open circles); (c) radius of gyrationRg versus molecular weight. (Reproduced by permission ofWiley-VCH from Antonietti et al..90/)

depends on the absorption of radiant energy of specificwavelengths by the chromophores. However, when thesolute particle size becomes comparable to the detectorwavelength, the output signal is considerably affectedby light scattering. Consequently, the measured signalmust be corrected in order to obtain an accurate

mass distribution..85/ The Mie theory.86/ used in thesecorrections takes into account the dependence of thescattered intensity on the particle size, the refractiveindex, and the scattering angles. Fluorescence detectionis most often used with derivatized samples..87/ A recentdevelopment in polymer characterization is the couplingof FFF with a multiangle light scattering (MALS)detector..88 – 91/ This hyphenated system combines thehigh resolution capabilities of FFF with the absoluteand independent molecular weight determination of lightscattering, thus eliminating the need to calibrate theFFF system. The absolute determination of molar massesby MALS also allows for small nonidealities in theoperating conditions such as fluctuations in temperatureand flow rate. The best results are obviously obtainedwhen optimum separation conditions are used and in theabsence of nonidealities. The high fractionating capabilityof FFF is registered as an increase in the relative molarmass along the eluted peak as shown in Figure 6(a–c). Theintegrated FFF MALS apparatus has also allowed an in-depth study of the effect of experimental conditions suchas injected sample mass or crossflow rate on the elutionand fractionation of polymer samples..92/ A detaileddiscussion on these topics may be found in sections 6.1 and6.2. The generally low sensitivity of laser light scatteringdetection is a problem, particularly for low-molecular-weight components and polyelectrolytes whose molarmass determinations are meaningful only at high ionicstrength..93/ This problem has been overcome by couplingan electrospray mass spectrometer to a FlFFF channel.56/

as mentioned in section 2.4.

4 EXPERIMENTAL PROCEDURES

4.1 Sample Preparation and Handling

No special treatment is generally required for the prepa-ration of samples to be analyzed by FFF. Specificprocedures, such as extraction, purification, and con-centration, may be necessary for polymers of naturalorigin since synthetic polymers undergo sample purifi-cation as part of the production process. As mentionedpreviously, the narrow sample pulse injected in an FFFchannel undergoes considerable changes in concentra-tion as it is relaxed and fractionated.81/ (see later). Theconcentration of the injected polymer sample solution istherefore a parameter that must be carefully controlled.Injection of large sample masses affect the plate height.94/

even before the effect of overloading is registered byother retention parameters. The sample concentrationduring relaxation depends on the mass injected and canbe one or more orders of magnitude higher than thatof the initial sample solution depending on the reten-tion ratio (concentration at the wall is approximately


equal to the sample concentration divided by l whichis expected to be �0.1). The effect of molecular dimen-sions on the concentration of polymer solutions is knownfrom theory. Four model polymer solutions are generallyidentified: the dilute solution corresponding to a con-centration of molecules separated by large volumes ofsolvent, the intermediate regime with a much reduceddistance between polymer chains that may touch eachother but still do not overlap, the semidilute, and theconcentrated regime. In the last two cases, the polymerconcentration is so high that chain entanglement dom-inates and the system may not be regarded as that ofindividual molecules suspended in a liquid medium. Thesolution properties are not governed by the propertiesof individual molecules and such systems will thereforehave a behavior very different from that of any concen-trated solution of small molecules. For this reason, theconcentration cŁ corresponding to that of the interme-diate regime has been the subject of several theoreticaland experimental investigations. In a number of studies,the dependence of cŁ on molecular weight was foundto follow a power law of the type cŁ /M�a, where ais ¾0.7..95 – 97/ From considerations of the polymer coildensity and volume fraction , it may be shown thatthe threshold value Ł for the transition between thedilute regime and the semidilute is related to the numberof repeat units N in the macromolecular chain and thesquare of a characteristic parameter d/l (the ratio betweenthe coil thickness d and its length l). An estimate of thevolume fraction Ł shows that the onset of the semidi-lute regime occurs at much lower concentration for moreelongated macromolecular chains. Theoretical findingsare corroborated by experiments when the behavior offlexible chain polymers, for which the d/l value is between1/2 and 1/3, is compared with that of DNA, which has avalue of ¾1/50. The critical concentration for this macro-molecule hence decreases 2500-fold. The experimentallydetermined critical concentration reported for DNA is2.2–2.6 µg per 100 µL..98,99/ An injection concentration100 times lower than the critical value is recommended inFFF experiments. For synthetic polymers, concentrationsof 0.05–0.50 g L�1 and injection volumes of 1–10 µL giveeasily detectable peaks under conditions of total samplerecovery..68/

4.2 Sample Injection and Relaxation

Sample solutions may be introduced into an FFF chan-nel through an injection valve with a constant-volumeloop such as those commonly used in chromatography orthrough an on-line tee-union fitted with a septum. Thelatter does not limit the injected volume but the poly-mer septum should be isolated from the channel with anon-line zero-dead-volume filter. When sample particles

are first introduced into the channel, they are dispersedover the entire cross-section and experience the samefield strength but different longitudinal migration veloc-ities depending on their distance from the accumulationwall. While under the effect of the field alone the sampleplug would concentrate in a narrow layer of exponentialconcentration. However, with displacement by the longi-tudinal flow, the plug undergoes a considerable dispersionalong the channel length. This happens because moleculesstarting their migration far from the accumulation wallwill take longer to reach the equilibrium position andwill be swept ahead of species closer to the accumulationwall. A simple way to circumvent this problem and greatlyreduce the relaxation contribution to the plate height isto halt the longitudinal flow as soon as the sample entersthe channel. This stop-flow procedure allows the fieldto complete the sample relaxation process without theundesirable effects of differential migration velocities..1/

The stop-flow time, tsf, depends on the channel thickness,the field strength, and the final transverse position of thezone’s center-of-gravity. It has limits for low and high l ofw2/2D and w2/12D, respectively. In practice, the relax-ation process is started when all sample molecules haveentered the channel. The delay time between the injectionand the beginning of the relaxation is given by the ratio ofthe volume of the tubing between the injection port andthe channel inlet and the volumetric flow rate. Althoughthe stop-flow procedure has proven successful in yieldingwell-shaped peaks at the expected retention times, it isassociated with a number of nonideal phenomena suchas sample loss due to adsorption on the accumulationwall, baseline disturbance and increased analysis time.Different channel designs have been adopted to achievesample relaxation without stopping the axial flow. A well-relaxed sample zone can rapidly form by applying a strongfield in a small area localized at the channel inlet or byreducing the channel thickness in the same region. Hydro-dynamic relaxation, currently applicable only to flowsystems, may be achieved by isolating the inlet portionof the depletion wall and applying a higher field strengthonly in that area..100/ Sample components entering thechannel are rapidly transported to the accumulation walland relaxed. This system has been mostly used for bio-logical macromolecules..101/ The pinched-inlet channel,applicable in principle to any FFF system,.102/ has beentested experimentally on latex particles in an FFF channelunder gravitational force..103/ Hydrodynamic relaxationobtained with a thin channel splitter.104/ has been exam-ined in SdFFF with latex particle samples..105/ Hybridsplit and frit-inlet FlFFF systems have been designed andtested..106/

The relaxation procedure in asymmetric FlFFF issomewhat different from that in a symmetrical system. Itmay be achieved virtually at any point along the channel


length by injecting sample material at a chosen distancefrom the channel inlet when two inflows of carrier liquidare introduced at both the channel inlet and outlet..72/

This procedure is termed ‘‘opposing flows relaxation’’.The two flows entering the channel through the inletand the outlet meet at a focusing point that dependson the ratio between the inlet flow rate and the sum ofthe inlet and outlet flow rates. The focusing point in anasymmetric channel may thus be adjusted by selectingthe flow rates. Alternatively, the flow entering throughthe inlet end may be eliminated so that only the reverseflow is maintained. This procedure defined ‘‘reverse flowrelaxation’’ allows the sample to migrate to the verybeginning of the channel and relax at the inlet point. Whenthe opposing flows relaxation is used sample material maybe loaded through either the inlet or the outlet or even anindependent port at a given point along the channel. Inthis case, an additional pump must be used. The opposingflows approach has given rise to the opposed flow sampleconcentration procedure which allows very large volumesof dilute sample to be loaded on to a FlFFF channel..107/

As much as 105-fold concentration has been reported (1-Lsample volume introduction). This sample concentrationtechnique can be applied to symmetrical, asymmetric, andhollow-fiber FlFFF. In the hollow-fiber FlFFF technique,sample relaxation is obtained much as in the asymmetricset-up by pumping opposing flows in from the inlet andoutlet while maintaining a constant radial flow.

4.3 Operation with Constant or Programmed Field

When complex mixtures have to be analyzed, differencesin the property of interest of the species under inves-tigation may be so large that no constant experimentalcondition may yield a satisfactory result for all speciesin a single run. This situation, well known in the chro-matography of complex natural mixtures, is circumventedin HPLC with the so-called gradient elution, where theeluent composition is changed with time. The basic con-cept of gradually decreasing the retention power in orderto let the most retained sample elute in a shorter time,thus gaining in detectability, has been applied to FFF..108/

Programmed field strength and/or flow rate are particu-larly useful for polydisperse samples whose elution wouldbe spread over a wide time interval because of the highsystem selectivity. In FFF, there is an almost unlimitednumber of programming choices considering that both thefield and the channel velocity may be varied as needed.In principle, the eluent composition may also be pro-grammed but this option has only been applied to thecarrier fluid density in SdFFF..108/ Both the fluid veloc-ity and field strength may follow a step, linear, quadratic,parabolic, or exponential time-dependent function. In anyof these forms of programming a period at constant con-ditions is usually applied to allow early-eluting particles to

undergo adequate retention and separation before start-ing the programmed decrease of the field or increase ofthe fluid velocity. It has been shown that the fractionatingpower is a convenient universal parameter for comparingthe effectiveness of different forms of programming. Thediameter-based fractionating power, Fd, or the molecular-weight-based FM, is defined as the resolution Rs of twosequentially eluting species divided by the relative dif-ference in their size or molecular weight..109/ Linear andparabolic decay programs,.64,110/ the first functions tobe investigated for polymer separations, resulted in aconsiderable improvement over a constant field strengthseparation. However, closer examination showed an ini-tial rise in Fd followed by a rapid decrease as the fieldstrength went to zero..111/ The exponential field decayprogram introduced by Kirkland et al..112,113/ for particlesize analysis by SdFFF has been applied to polymer sepa-rations by FlFFF.114/ and ThFFF..110,115 – 117/ This type ofprogram also resulted in an initial increase of the frac-tionating power followed by a strong decrease..109/ Onlya power-law dependence of the field decay proposed byWilliams and Giddings.118/ yielded a constant molecular-based fractionating power for a wide range of molecularweights..119/

5 APPLICATIONS

5.1 Organic-soluble Polymers

The high versatility of FFF has proven suitable to so manyapplications in different fields that a complete surveywould be impossible. We therefore choose to report hereonly selected examples of the most innovative and recentapplications. Many others may be found in the literature.

ThFFF with field-strength programming has been usedto separate PS standards with molecular weights spanning4000–7 100 000 Da. In Figure 7(a), the T follows aparabolic function that decreases from 70 to 0 °C..110/

Since this early ThFFF work, the analysis time has beendramatically reduced to 20 min without significant lossof resolution by the advent of new instrumentation andthe introduction of the power program function..119/ Anapplication of this form of programmed elution is shownin Figure 7(b).

Although FFF was conceived as a separative technique,its rigorous theoretical background has demonstrated thatmeasurements of fundamental physicochemical proper-ties may be very accurate and in some cases unachievableby other techniques. This is the case for investigationsof the thermal diffusion of polymers and copolymers andtheir correlation with the polymer and solvent chemicalcomposition. Studies in this field showed a linear relation-ship between the thermal diffusion coefficient DT and the


1 h 6 h

70°C

Inject

4k20k97k

51k

200k

411k 860k 1800k 7100k

∆T(a)

80°C

13°C

∆T

t 0 35 k

90 k

200 k

400 k

900 k

3800 k

0 5 10 15 20

Time (min)(b)

Res

pons

e

Figure 7 Separation of two mixtures of PS standards in asimilar molecular weight range with field strength decay.(k D kDa) (a) Parabolic programming. (Reprinted with permis-sion from J.C. Giddings, L.K. Smith, M.N. Myers, Anal. Chem.,48, 1587–1592 (1976). Copyright 1990, American ChemicalSociety.) (b) Power programming. (Reprinted with permissionfrom M. Myers, P. Chen, J.C. Giddings, ACS Symp. Ser., 521,47–62 (1993). Copyright 1993, American Chemical Society.)

temperature at the center of the sample zone for PS inethylbenzene.36/ and a similar correlation between DT

and the mole fraction of one of the monomers in randomcopolymers..120/ This finding has a number of implications,one of which is that ThFFF has an additional separatingdimension that allows samples to be resolved accordingto chemical composition as well as hydrodynamic size.This is shown in Figure 8, where the diblock copolymerpoly(styrene-co-isoprene) is separated from the triblockof same size poly(styrene-co-isoprene-co-styrene) only byThFFF. Hydrodynamic chromatography (HDC), anotheranalytical technique for polymer separations, has a higherefficiency than FFF but, like GPC, discriminates samplesonly by size. Consequently, fractions of PS, polyiso-prene and polybutadiene (PB) with similar hydrodynamicdimensions are only partially separated by HDC whereasthey are completely resolved by ThFFF.121/ because of

0 10 20 30 40

Time (min)

Res

pons

e

p(SI)2 + p(SIS)l Void peak

ThFFF

Void peak

p(SI)2

p(SIS)l

GPC

Figure 8 Co-elution of a sample of diblock copolymer ofpoly(styrene-co-isoprene) and triblock poly(styrene-co-isoprene-co-styrene) from a GPC column and separationof the same mixture by ThFFF based on the difference inthermal diffusion coefficient. (Reprinted from Cho et al.,.71/ bycourtesy of Marcel Dekker Inc.)

their different thermal diffusion coefficients. Althoughretention in ThFFF is dependent on DT, the evaluation ofabsolute values of this parameter is not straightforwardsince the measurable retention parameter l yields valuesof D/DT. DT alone may therefore be determined only ifthe diffusion coefficient is measured by an independenttechnique. One approach is to couple SEC to ThFFFand determine D using light scattering. This multidi-mensional approach allows the fractionation of polymersamples according to size by SEC and to thermal diffu-sion by ThFFF..122,123/ The usefulness of the combinedSEC/ThFFF technique is demonstrated in the analysis ofpolydisperse samples of copolymers whose relative com-position, which may vary with molecular weight, givesrise to materials with different properties. The prelim-inary fractionation of a polydisperse sample of PS bySEC may occur with a selectivity of 0.15 in the molecularweight range 150 000–1 000 000 Da and drops to 0.04 forlower M fractions..122/ This selectivity, well below thatcommonly found in FFF, is obtained after a system cali-bration with well-characterized PS fractions and the light-scattering determination of diffusion coefficients. Thethermal diffusion coefficient, calculated from retentionmeasurements once both molecular weight and ordinarydiffusion coefficients are known, is generally independentof molecular weight..124/ Fractionation according to


8(a) 10 12 14 16 18 2220

1 2 3 4 5 6 7 8 9

SEC

Time (min)0 2 4 6 8 10 12 14

2

(b)

3

4

5

6

7

8

9

B

BB

B A

B

B

A

A

C

B C

A

A

AAB

BB A

ThFFF

Figure 9 (a) Size exclusion chromatogram of a blend of PS,PB and PTHF and (b) ThFFF of individual fractions takenafter the SEC elution. Numbers along the y-axis of the ThFFFfractogram correspond to the labeled SEC fractions in (a).(Reprinted from A.C. van Asten, R.J. van Dam, W.Th. Kok,R. Tijssen, H. Poppe, J. Chromatogr. A, 703, 245–263 (1995).Copyright 1995, with permission from Elsevier Science.)

differences in thermal diffusion coefficient alone givesinformation on the copolymers’ chemical composition.Figure 9(a) and (b) show the partial fractionation (a)by SEC of a blend of PS, PB, and polytetrahydrofuran(PTHF) and then (b) by ThFFF of some SEC fractionscollected at different retention times. The ThFFF frac-togram indicates the presence of different polymer species(fractions 3–6) whose measured DT are in good agree-ment with values of the corresponding PB and PTHFhomopolymers determined by ThFFF and light scatter-ing, e.g. 0.22ð 10�7 and 0.47ð 10�7 cm2 s�1 K�1 versus0.23ð 10�7 and 0.50ð 10�7 cm2 s�1 K�1..125/

The measurement of the thermal diffusion coefficienthas become a key step in the determination of copoly-mer relative chemical composition. Two styrene–methylmethacrylate copolymers with different styrene contentanalyzed by SEC/ThFFF.122/ show different DT versusretention time trends when analyzed by ThFFF, althoughthe SEC traces are almost identical. Using a calibra-tion plot for the SEC column based on PS standards(which is not a rigorous procedure), the fractions may beassigned a molecular weight and DT may be related to thisparameter. The invariant trend of the thermal diffusioncoefficient of one sample and the clearly increasing valuesof the second sample suggest that the styrene percentage

is different and that it increases with M in the secondcase..122/ Increasing DT with increasing weight fractionsof vinyl acetate is reported for poly(ethylene-co-vinylacetate) copolymers..83/ Multidimensional analysis mayalso be obtained by coupling a ThFFF system withHDC..126/ Samples with the same D/DT eluting from theThFFF system are subsequently fractionated accordingto size by HDC.

ThFFF appears to be the only separation techniquesuitable for the analysis of gels and rubbers.82,90,127/

because irreversible adsorption evident in other methodsis minimized..90,127/ In addition, the need to filtersamples prior to their injection into a GPC columnresults in the removal of high-molecular-weight polymercomponents as well as of the gel. This causes the averagemolecular weight and molecular weight distributions tobe consistently lower in GPC than in ThFFF..127/ Theopen FFF channel design eliminates the problem ofplugging that is encountered in GPC when gel containingsamples are not filtered before the analysis. Hencepolymer and gels may be completely separated withina single run by ThFFF,.128/ as shown in Figure 10.

0 20 40 60 80

Time (min)

Res

pons

e

∆T = 90 K

∆T = 5 K

∆T profile

Void + soluble polymer

Rubber particles

Figure 10 Separation and characterization of the polymer andgel components present in acrylonitrile–butadiene–styreneplastics. (Reproduced from P.M. Shiundu, E.E. Remsen, J.C.Giddings, J. Appl. Polym. Sci., 60, 1695–1707 (1996). Copyright 1996, John Wiley & Sons, Inc. Reprinted by permission ofJohn Wiley & Sons, Inc.)


Molecular weight and particle size distributions arecalculated for both the polymer and the gel components.Although other techniques have been used successfullyto analyze gels and rubbers, SEC has been consideredthe separative methodology par excellence in spite ofits limitations..129,130/ It was shown that the differentDT values for different polymers have been exploitedin the ThFFF analysis of core-shell latex particles..131/

The retention time is sensitive to the composition ofthe polymer shell. A calibration curve may be drawnto relate retention time and percentage of methacrylicacid in the shell. The sensitivity of DT to the particlesurface composition is further illustrated using similarsized particles of different polymeric and inorganicsurfaces..132,133/

5.2 Water-soluble Polymers

Early studies in ThFFF.37/ showed that different organicsolvents had a very similar effect on the retention ofpolymers. In contrast, when water is used as the carrierliquid, the thermal diffusion factor a is very low andretention is negligible unless a considerable amount ofsome organic solvent (¾60%) is present. Except for a fewresults confirming the poor retention in such a solvent,.117/

water-soluble synthetic polymers have been analyzed bythe most versatile technique of the FFF category, FlFFF.This technique was recognized since its first appearance ashighly suited to polymer fractionation..134,135/ Althoughresolution and analysis time were not optimized, theearly results allowed the determination of molecularparameters, such as hydrodynamic size, on the basis oftheoretical concepts that have subsequently been exten-sively confirmed. Polyacrylamide (PAAm) is a widelyemployed polymer in many fields that is difficult to char-acterize and fractionate. Commercially available frac-tions of PAAm generally have a broad distribution..136/

The FlFFF fractograms of the three PAAm samplesillustrated in Figure 11 consistently show the presenceof low-molecular-weight components in each polymersample..68/ A similar peak asymmetry is also observed forbroadly disperse samples in organic solvents..63/ As men-tioned earlier (section 2.4), in the absence of an absolutetechnique for the molar mass determination, the molec-ular weight distribution may be accurately determinedby calibration. The calibration procedure, however,should be performed with narrowly distributed, well-characterized standards of closest possible chemical com-position to the unknown. When standards with these char-acteristics are not available, absolute measurements of thediffusion coefficient may be used to evaluate the polymerhydrodynamic size using the Stokes–Einstein equation.The absence of non-ideal sample–wall interactions on theelution of PAAm is verified by comparing measurements

0 50 100 150

80 k500 k

1400 k

t0 Time (min)

Hydrodynamic size (nm)

Poly(ether sulfone)membrane

Cellulosemembrane

80 000500 000

1 400 000

122849

122954

Figure 11 FlFFF separation of three samples of PAAmof different nominal molecular weight. The hydrodynamicdiameters were determined using two different membranes.(Reproduced from M.-A. Benincasa, J.C. Giddings, J. Microcol.Sep., 9, 479–495 (1997). Copyright 1997, John Wiley & Sons,Inc. Reprinted with permission of John Wiley & Sons, Inc.)

made in solutions of identical ionic strength but withmembranes of different composition, namely poly(ethersulfone) and cellulose..137/

As discussed in the theory section, the overall poly-mer molecular dimensions are anticipated to depend,to a certain extent, on the properties of the surround-ing medium. This effect is expected to be enhancedfor charged polymers. The effect of solvent and ionicstrength was identified in the first study in FlFFF ofwater-soluble polymers..135/ Poly(ethylene oxide) (PEO),a polymer widely used in biomedical and biotechnologicalapplications because of its non-toxicity, shows an almostideal correlation between the measured diffusion coef-ficient and molecular weight in aqueous sodium sulfatesolutions..69/ Similar to the observation reported by Has-sellov et al.,.56/ this correlation is found for polymers withmolecular weights well below the range for which thegeneral polymer scaling laws are expected to hold. Thecorrelation between diffusion coefficient and molecularweight in potassium sulfate is very different to that insodium sulfate. The authors attribute this difference tothe capability of low-molecular-weight PEO fractions toform complexes with some metal cations, as reported inindependent studies..138/ The elution profiles of PEO sam-ples in a molecular weight range 250 000–1 000 000 Damay be obtained by FlFFF with good resolution asshown in Figure 12. Charged amphiphilic graft copoly-mers are a particular type of sample that may dramat-ically change their conformation in different solventsbecause of the presence of hydrophilic and hydrophobic


0 25 50 75

250 000

590 000

990 000

t 0 Time (min)

Figure 12 Separation of three PEO samples by FlFFF inaqueous 0.025 M Na2SO4.

moieties derived from different homopolymers. In aque-ous solutions, they form a hydrophobic core with thehydrophilic moieties on the surface. At low pH and in thepresence of salts, aggregation may occur for the copoly-mer of styrene, methyl methacrylate and maleic anhydridewith grafts of poly(ethylene oxide) monomethyl ether(MPEO)..139/ The polymer molecular conformation andsolubility in water depend on the pH, which affects dis-sociation of the carboxyl groups, and on the solventionic strength. An extended conformation may exist athigh pH or aggregation may occur at low pH and highionic strength. The copolymer hydrodynamic diameterincreases with decreasing pH. This effect is attributed tothe formation of aggregates of less charged copolymersat low pH, a phenomenon that seemed amplified whenlong stop-flow times are used. When a ca. 0.002 M buffersolution is used as the carrier liquid, the molecular dimen-sions are considerably higher (16–40 instead of 2–20 nm)than those measured in unbuffered solutions. It is pos-tulated that the buffer salts cause shielding of chargedsites which consequently promote aggregation throughhydrophobic interactions of the polymer backbone. For-mation of aggregates is evidenced by the particle sizedistributions shown in Figure 13..140/

SdFFF is a technique usually associated with parti-cle rather than polymer analysis. The maximum fieldstrength or centrifuge speed of currently available com-mercial instruments is insufficient to induce transport ofthe polymers to their equilibrium positions at the accu-mulation wall. Consequently, retention and separationby SdFFF are poor. However, an instrument with high-field-strength capabilities can be used to characterizehigh-molecular-weight polymers..141/

0 5 10 15 20 25 30 35 40 45

dH (nm)

Abs

orba

nce

A

B

C

D

0.002 AU

Figure 13 FlFFF-derived particle size distributions of anamphiphilic grafted copolymer poly(styrene-co-methyl metha-crylate-co-maleic anhydride) and MPEO. Aggregation isobserved as the sodium sulfate concentration is increased. Thecarrier liquids used were (A) pure water, (B) 1 µM Na2SO4,(C) 10 µM Na2SO4, and (D) 100 µM Na2SO4. (Reprintedwith permission from B. Wittgren, K.-G. Wahlund, H. Derand,B. Wesslen, Langmuir, 12, 5999–6005 (1996). Copyright 1996,American Chemical Society.)

6 METHOD DEVELOPMENT

6.1 Determining Experimental Conditions

Before starting an analysis, specific requirements maybe set for a number of experimental parameters suchas analysis time, resolution, and selectivity. A thoroughdiscussion of this topic would require a long navigationthrough FFF theory and is beyond the scope of this article.Therefore, some practical recommendations are givenhere with reference to theoretical fundamentals on whichthey are based. Demonstration of these concepts may befound in the specific literature and will not be dealt withhere. A generally desired characteristic is short analysistimes. The retention time in FFF is linearly related to theapplied field strength, ceteris paribus. This translates intoa dependence on the temperature gradient, crossflow rate,solvent viscosity, channel thickness, and void volume.


Although in theory values of these parameters maybe accurately determined, common laboratory practicehas shown that void volume V0 and channel thicknessdetermination in FlFFF is not a trivial procedure. Apeak breakthrough technique.142/ has been proposed thatallows the determination of the channel void time, andrelated volume, from the time needed for an unretainedsample to emerge from the channel under high-flow-rateconditions. Experiments must be carried out with greatcare and in the total absence of a crossflow. A simpleway to ensure this is to block the crossflow inlet andoutlet. More accurate void volume determinations maybe obtained by sandwiching the spacer and the membranebetween two glass plates with holes drilled through oneof the plates to act as the channel inlet and outlet. Thedetermination of the actual void volume in FlFFF may notbe bypassed since it also yields a measure of the channelthickness. This last parameter is the most critical in FlFFFsince the retention time varies with w2. Molecular weightmeasurements, obtained from retention parameters, arestrongly affected by the channel thickness. The crossflowrate PVc and channel flow rate PV have opposing effects ontr since they contribute as the ratio PVc/ PV. An increase inthe two flow rates which does not alter this ratio wouldhave no effect on tr. However, l and t0 would decrease.This would translate into a decrease of the retention ratiot0/tr and a higher compression of the sample zone with agreater probability of overloading and sample interactionwith the accumulation wall. Resolution, which dependson . PV3

c / PV/1/2, would increase with the 3/2 power of thecrossflow rate and decrease with the 1/2 power of thechannel flow rate. Studies on the effect of field strengthand injected sample load on polymer fractionation byFlFFF have shown that the molar mass distribution seemsto broaden with increasing crossflow rates or decreasinginjected sample loads..92/ Unlike ThFFF, where the flowprofile is considerably affected by the field, perturbationsdue to the crossflow in FlFFF are negligible..143/ Ingeneral, axial flow rates of 0.2–2 mL min�1 are used forpolymer analysis. Low flow rates and velocities protectsamples from shear degradation and peak broadening dueto the nonequilibrium contribution to the plate height thatdepends linearly on the flow velocity.

Unlike FlFFF, the retention time in ThFFF does notdepend directly on the channel thickness. It dependson the void time t0, which is related to w. Theretention time is a function of the thermal gradientdT/dx, which can be increased by reducing w orincreasing the hot wall temperature. The first approachis useful when the working temperature is above thesolvent boiling point and further pressurization of thesystem to elevate the boiling point.3/ is not an option.However, the reduction of w in ThFFF is limited byheat transfer that may require substantial heat fluxes

between the hot and cold walls. In addition to theprevious considerations, w affects resolution and sampledilution in all the FFF techniques. Generally, 90–99% ofthe FFF channel volume is occupied by pure solventduring elution. The injected sample is hence verydiluted on elution from the FFF channel. This effectmay be reduced using stream splitters.104/ or frit outletsystems..100/ All channel dimensions may in principlebe varied. An increase or reduction of either b orL has some advantages and some disadvantages. Anextensive discussion on the theoretical and practicalaspects of changing these dimensions is reported inthe literature..144/ The dimensions of asymmetric FlFFFchannels are subject to more constraints..145/ Commonlyused channel flow rates in ThFFF are of the same order ofmagnitude as those used in FlFFF. Data collected over a15-year period using a number of different channels haveshown that retention in ThFFF is affected by the absolutevalue of the cold wall temperature Tc..146/ Higher Tc

values lead to lower retention with the sameT. The useof binary solvents in ThFFF has been shown to enhanceretention considerably in some cases. This result may beused to extend the range of applicability of ThFFF towardlower molecular weight limits..147/

6.2 Effect of Sample Size

Sample size effects on retention were described inearly FFF studies..135/ These effects, common to otherseparation techniques, manifest themselves in FFF asdistortions of the elution profile and shifts in retentiontime that cannot be related to any sample physicochemicalproperty but rather to the amount of sample injected.It was also recognized in the early FFF work that theionic strength changes remarkably the effect of sampleload on retention time..135,148/ The effect of sample loaddepends on the polymer–solvent system rather thanon the FFF technique employed. The general trendof increasing retention time with increasing injectionamount is observed for FlFFF and ThFFF of PS inethylbenzene and tetrahydrofuran..81,149/ In this casethe role of molecular weight in enhancing the effectof load even at very low T values was shown.Longer retention times are also reported for higheramounts of PTHF analyzed in toluene by ThFFF..150/

The opposite trend is found in aqueous separationsof particles by SdFFF.148/ and for synthetic.65,68,135/

and biological polymers..151/ The dependence of sampleoverloading on the physicochemical properties of thepolymer–solvent system rather than on the analyticaltechnique is substantiated by the findings that aqueoussynthetic and biological polymer systems also show adecrease in retention time with increase of load in


hollow-fiber FlFFF..152,153/ The observed decrease inretention time with increasing sample load for particlesand charged polymers has been explained on the basis ofexcluded volume effects. For systems where the samplevolume fraction is not negligible, l values are expectedto be higher than those predicted from standard FFFtheory, which assumes infinitely small non-interactingspecies..154/ Since both the interparticle electrostaticrepulsion and chain expansion due to intramolecularrepulsion contribute to an increase in the effectivevolume occupied by the sample species, an enhancedoverloading effect is expected for charged particles.In contrast, a depression of the phenomenon may bepredicted with a reduction of the electrostatic effects. Itfollows that the ionic strength of the carrier liquid shouldconsiderably affect the onset of sample overloading. Highionic strength is expected to reduce both the overallmolecular dimensions of flexible-chain macromoleculesand the double-layer thickness. The reduction of theseparameters decreases the effective sample volume toa greater extent than the lower solvating power ofa concentrated salt solution alone. Experiments onsynthetic water-soluble polymers show that the ionicstrength.65/ and the type of electrolyte added to the carrierliquid may affect the relationship between sample size andretention..69,139/

6.3 Membranes in Flow Field-flow Fractionation

A unique feature of the FlFFF system is the semiperme-able membrane that is laid over the frit and serves as theaccumulation wall. The possibility of wrinkling or swellingof the membrane and uncertainties in the performanceof the different polymer materials used in their fabrica-tion have been the main deterrent in the developmentof FlFFF. The membrane used in the FlFFF channelmust meet a number of specific requirements not nec-essarily fulfilled by commercially available membranes.The pore size and the pore density, i.e. the number ofpores per unit area, have to be uniform. Inhomogeneouspore density leads to regions of nonuniform permeabil-ity and crossflow rate. The nominal and effective poresizes are often given by the manufacturer. While thefirst is an absolute measurement obtained by electronmicroscopy, the second must be considered an indica-tion of the membrane performance with respect to thespecific probe and to the conditions used for this deter-mination and may not be directly transferred to sampleswith different physicochemical properties. For example,the Celgard isotactic polypropylene membrane is mar-keted with a nominal pore size of 50 nm and an effectivepore size of 20 nm, but samples of much smaller diam-eter are retained..65/ It is known that filtration through

a membrane is not a purely mechanical process andthat a number of parameters contribute to the samplepermeation or retention by a membrane. A higher per-centage of latex particles of considerably smaller diameterthan that of PS samples in tetrahydrofuran are retainedby a polytetrafluoroethylene (PTFE) membrane with anominal 20-nm pore size..155/ A regenerated cellulosemembrane from Millipore with a 10 000 molecular weightcut-off (MCO) retains PEO samples in the 4000–1 000 000molecular weight range whereas a membrane of the samematerial and from the same supplier with a lower cut-offshows no elution of the PEO samples..156/ Considering thelower MCO, it may be inferred that adsorption occurredin this case. Specific tests to check sample permeationthrough the membrane are always recommended, how-ever. They may be carried out by connecting the crossflowoutlet to a detector and monitoring the eluted carrier liq-uid for the presence of sample. The general scarcity ofmembranes capable of withstanding organic solvents hasbeen one of the main limitations in the application ofFlFFF to organosoluble polymers. Cellulose nitrate gavea good performance in the first experiments of FlFFFin ethylbenzene,.81/ but many more membrane materialscompatible with organic solvents such as fluoropolymers,polyvinylidene, polyaramide and PTFE are now commer-cially available..155/

Ultrafiltration membranes such as those commonlyused in FlFFF may be classified as cellulosic andnoncellulosic. Cellulose and its derivatives were oneof the first materials employed as a semipermeablemembrane and successfully used in the FlFFF analysisof aqueous systems of proteins, synthetic hydrophilicpolymers, and latex particles. Cellulosic ultrafiltrationmembranes are available in a variety of MCOs andare cast on a thicker, more permeable support material.The presence of this support adds robustness and easeof handling to the membrane. Thin-film (5–25 µm)unsupported membranes, most often noncellulosic, aremore difficult to handle but their flexibility allowseasy positioning on the frit wall. Unlike cellulosicultrafiltration membranes, these mainly hydrophobicmembranes do not allow wicking of carrier liquid outof the area of permeation (no leaking). An ample varietyof membranes used with various solvents and samples islisted in Table 1. Besides preliminary considerations onthe physicochemical properties of both the membranematerial and the sample to be analyzed, an unambiguousanswer on the performance of a membrane is given bya test of the absolute sample recovery..68,137,157/ This isaccomplished by comparing the peak area of the outputsignal of a regular FFF run with the area acquiredupon injecting the same sample amount through anopen tube.


Table 1 Summary of membrane materials and their applications in FlFFF

Membrane material Sample Carrier composition

Acrylic copolymer Proteins, lipoproteins Aqueous solutionCellulose PAAm, humics Aqueous solutionCellulose acetate Viruses, proteins Aqueous solutionCellulose nitrate PS EthylbenzeneFluoropolymer PS TetrahydrofuranPolyamide Polyethylene, Xylene

toner pigment ToluenePolyaramide PS TetrahydrofuranPolycarbonate Antibodies, proteins, Aqueous solution

humic and fulvic acidsPolyelectrolyte complex Proteins, viruses Aqueous solutionPoly(ether sulfone) PAAm, Aqueous solution

PEO,Poly(styrene sulfonate),PS, carbon black, Xylene, cyclohexanePolyethylene Xylene

Poly(ethylene terephthalate) Proteins Aqueous solutionPoly(phenylene oxide) PS TetrahydrofuranPolypropylene, isotactic Poly(styrene sulfonate), Aqueous solution

polyvinylpyridine, proteinsPolysulfone Minerals, cells, humic and Aqueous solution

fulvic acids, poly(styrenesulfonate), dextrans, latex

PTFE PS, PEO, latex, silica Tetrahydrofuran,acetonitrile

Polyvinylidene PS TetrahydrofuranRegenerated cellulose Algae, bacteria, Aqueous solution

amphiphilic copolymers,DNA, hemoglobin,microspheres, lipoproteins,liposomes, nucleic acids,plasmids, pollens,polysaccharides, PEO, Tetrahydrofuranribosomes, silicas,Poly(methyl methacrylate)

Regenerated cellulose, PEO Ammonium acetate inmodified methanol solution

Literature related to the applications reported here may be found elsewhere..137,155,157,158/

ACKNOWLEDGMENTS

K.R.W. acknowledges support from the Colorado Schoolof Mines by a start-up grant for this work.

LIST OF SYMBOLS

a axis of prolate or oblate particlesA constant defined by DMb

b axis of prolate or oblate particlesb field-flow fractionation channel breadthb exponent in diffusion coefficient expressionB empirical constant in Equation (22)c particle or molecule concentrationc0 particle or molecule concentration

at the wall

c.tr/ time-dependent sample massconcentration at elution

d width of polymer chainD diffusion coefficientD0 diffusion coefficient at infinite dilutionDT thermal diffusion coefficientf friction coefficientf0 friction coefficient of an isolated sphereFd diameter-based fractionating powerFm molecular weight-based fractionating powerH plate heightHi instrumental contribution to plate heightHl longitudinal diffusion contribution to plate

heightHn nonequilibrium contribution to plate heightHp polydispersity contribution to the plate

height


Hr relaxation contribution to plate heightJx flux of particlesk Boltzmann constant` sample mean layer thicknessl length of polymer chainL channel lengthm.M/ mass distribution as a function of molecular

weightM molecular weightM0 molecular weight of repeat unitdM difference in molecular weight intervalMw weight-average molecular weightMN number-average molecular weightn exponent in Equation (24)N number of repeat unitsR retention ratio in Equation (6)Re equivalent sphere radiusRg radius of gyrationR0 spherical particle radiusRs resolutionSM molecular weight selectivityt0 void timetr retention timedtr retention time differencedtr/dM scale correction functiontsf stop-flow timeT absolute temperatureTc cold wall temperatureT temperature difference across the

channelU field-induced velocityPV volumetric flow ratePVc volumetric cross flow rateV0 void volumeVr retention volumehvi mean fluid velocityvp zone migration velocityw channel thickness

Greek charactersa thermal diffusion factorb exponent in thermal diffusion

Equation (22)g thermal expansion coefficienth fluid viscosityl retention parameterµ molecular weight polydispersity coefficient in Equation (24) or polymer

volume fraction (section 4.1)

ABBREVIATIONS AND ACRONYMS

CFFF Concentration Field-flow FractionationElFFF Electrical Field-flow Fractionation

FFF Field-flow FractionationFlFFF Flow Field-flow FractionationGPC Gel Permeation ChromatographyHDC Hydrodynamic ChromatographyHPLC High-performance Liquid ChromatographyMALS Multiangle Light ScatteringMCO Molecular Weight Cut-offMPEO Poly(ethylene oxide) Monomethyl EtherPAAm PolyacrylamidePB PolybutadienePEO Poly(ethylene oxide)PS PolystyrenePTFE PolytetrafluoroethylenePTHF PolytetrahydrofuranSdFFF Sedimentation Field-flow FractionationSEC Size-exclusion ChromatographyThFFF Thermal Field-flow Fractionation

RELATED ARTICLE

Biomolecules Analysis (Volume 1)High-performance Liquid Chromatography of BiologicalMacromolecules

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65. M.-A. Benincasa, J.C. Giddings, ‘Separation and Molec-ular Weight Distribution of Anionic and CationicWater-soluble Polymers by Flow Field-flow Fraction-ation’, Anal. Chem., 64, 790–798 (1992).

66. J.C. Giddings, M.-A. Benincasa, M.-K. Liu, P. Li, ‘Sep-aration of Water Soluble Synthetic and BiologicalMacromolecules by Flow Field-flow Fractionation’, J.Liq. Chromatogr., 15, 1729–1747 (1992).

67. J.E.G.J. Wijnhoven, J.P. Koorn, H. Poppe, W.Th. Kok,‘Hollow-fiber Flow Field-flow Fractionation of Polysty-rene Sulfonates’, J. Chromatogr. A, 699, 119–129(1995).

68. M.-A. Benincasa, J.C. Giddings, ‘Separation and Char-acterization of Cationic, Anionic, and Nonionic Water-soluble Polymers by Flow FFF: Sample Recovery,Overloading, and Ionic Strength Effects’, J. Micro. Sep.,9, 479–495 (1997).

69. M.-A. Benincasa, K.D. Caldwell ‘Flow FFF of Poly(ethy-lene Oxide). Effect of Carrier Ionic Strength andComposition’, Macromolecules, in preparation.

70. M.N. Myers, ‘Considerations in Thermal FFF’, lecturepresented at the 7th International Symposium on Field-flow Fractionation, Salt Lake City, UT, 8–11 February1998.

71. K.-H. Cho, Y.H. Park, S.J. Jeon, W.-S. Kim, D.W. Lee,‘Retention Behavior of Copolymers in Thermal Field-flow Fractionation and Gel Permeation Chromatogra-phy’, J. Liq. Chromatogr. Relat. Technol., 20, 2741–2756(1997).

72. K.-G. Wahlund, J.C. Giddings, ‘Properties of an Asym-metric Flow Field-flow Fractionation Channel HavingOne Permeable Wall’, Anal. Chem., 59, 1332–1339(1987).


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78. J.C. Giddings, F.J. Yang, M.N. Myers, ‘Flow Field-flowFractionation as a Methodology for Protein Separationand Characterization’, Anal. Biochem., 81, 395–407(1977).

79. R. Beckett, Z. Jue, J.C. Giddings, ‘Determination ofMolecular Weight Distribution of Fulvic and HumicAcids Using Flow Field-flow Fractionation’, Environ.Sci. Technol., 21, 289–295 (1987).

80. J. Li, K.D. Caldwell, ‘Improved Accuracy in the Deter-mination of Field-flow Fractionation Elution Volumes’,J. Chromatogr., 555, 260–266 (1991).

81. K.D. Caldwell, S.L. Brimhall, Y. Gao, J.C. Giddings,‘Sample Overloading Effects in Polymer Characteriza-tion by Field-flow Fractionation’, J. Appl. Polym. Sci.,36, 703–719 (1988).

82. S. Lee, ‘Gel-content Determination of Polymers UsingThermal Field-flow Fractionation’, ACS Symp. Ser., 521,77–88 (1993).

83. S.J. Jeon, D.W. Lee, ‘Thermal Diffusion and MolecularWeight Calibration of Poly(Ethylene-co-Vinyl Acetate)sby Thermal Field-flow Fractionation’, J. Polym. Sci.: PartB: Polym. Phys., 33, 411–416 (1995).

84. J.J. Kirkland, S.W. Rementer, W.W. Yau, ‘PolymerCharacterization by Thermal Field-flow Fractionationwith a Continuous Viscosity Detector’, J. Appl. Polym.Sci., 38, 1383–1395 (1989).

85. F.-S. Yang, K.D. Caldwell, J.C. Giddings, ‘Colloid Char-acterization by Sedimentation Field-flow Fractionation.II. Particle Size Distribution’, J. Colloid Interface Sci.,92, 81–91 (1983).

86. M. Kerker, The Scattering of Light, Academic Press, NewYork, 1969.

87. S.K.R. Williams, R.G. Keil, ‘Monitoring the Biologicaland Physical Reactivity of Dextran Carbohydrates inSeawater Incubations Using Field-flow Fractionation’,J. Liq. Chromatogr. Relat. Technol., 20, 2815–2834(1997).

88. H. Thielking, W.-M. Kulicke, ‘On-line Coupling of FlowField-flow Fractionation and Multiangle Laser LightScattering for the Characterization of Macromoleculesin Aqueous Solution as Illustrated by Sulfonated

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89. D. Roessner, W.-M. Kulicke, ‘On-line Coupling ofFlow Field-flow Fractionation and Multiangle LaserLight Scattering’, J. Chromatogr. A, 687, 249–258(1994).

90. M. Antonietti, A. Briel, C. Tank, ‘ChromatographicCharacterization of Complex Polymer Systems withThermal Field-flow Fractionation’, Acta Polym., 46,254–260 (1995).

91. J. Lou, M.N. Myers, J.C. Giddings, ‘Separation of Poly-saccharides by Thermal Field-flow Fractionation’, J. Liq.Chromatogr., 17, 3239–3260 (1994).

92. B. Wittgren, K.-G. Wahlund, ‘Effects of Flow-rates andSample Concentration on the Molar Mass Characteri-zation of Modified Cellulose Using Asymmetrical FlowField-flow Fractionation–Multiangle Light Scattering’,J. Chromatogr. A, 791, 135–149 (1997).

93. K.S. Schmitz, Dynamic Light Scattering by Macro-molecules, Academic Press, New York, 1990.

94. J.C. Giddings, G. Karaiskakis, K.D. Caldwell, ‘Concen-tration and Analysis of Dilute Colloidal Samples bySedimentation FFF’, Sep. Sci. Technol., 16, 725–744(1981).

95. M. Adam, M. Delsanti, ‘Dynamical Properties of Poly-mers Solutions in Good Solvents by Raleigh ScatteringExperiments’, Macromolecules, 10, 1229 (1977).

96. K. Kubota, K.M. Abbey, B. Chu, ‘Static and Dynam-ical Properties of Polymer Solution with Upper andLower Critical Solution Points. NBS 705 Polystyrene inMethylacetate’, Macromolecules, 16, 137–143 (1983).

97. T.L. Yu, H. Reihanian, J.G. Southwick, A.M. Jamieson,‘Effect of Chain Overlap on Translational Diffusionof Polystyrene in Tetrahydrofuran’, J. Macromol. Sci.Phys., B18, 771–785 (1981).

98. W.W. Graessley, ‘Polymer Chain Dimensions and theDependence of Viscoelastic Properties on Concentra-tion, Molecular Weight and Solvent Power’, Polymer,21, 258–262 (1980).

99. J.Y. Ostashevsky, C.S. Lange, ‘The Effect of Solvent Vis-cosity and Temperature on DNA Viscoelastic Behavior’,Biopolymers, 25, 291–306 (1986).

100. J.C. Giddings, ‘Hydrodynamic Relaxation and SampleConcentration in Field-flow Fractionation Using Per-meable Wall Elements’, Anal. Chem., 62, 2306–2312(1990).

101. P. Li, M. Hansen, J.C. Giddings, ‘Separation of Lipopro-teins from Human Plasma by Flow Field-flow Fractiona-tion’, J. Liq. Chromatogr. Relat. Technol., 20, 2777–2802(1997).

102. J.C. Giddings, ‘A Pinched Inlet System for ReducedRelaxation Effects and Stopless Flow Injection in Field-flow Fractionation’, Sep. Sci. Technol., 24, 755–768(1989).

103. M.H. Moon, M.N. Myers, J.C. Giddings, ‘Evaluation ofPinched Inlet Channel for Stopless Flow Injection in


Steric Field-flow Fractionation’, J. Chromatogr., 517,423–433 (1990).

104. J.C. Giddings, ‘Optimized Field-flow Fractionation Sys-tem Based on Dual Stream Splitters’, Anal. Chem., 57,945–947 (1985).

105. S. Lee, M.N. Myers, J.C. Giddings, ‘HydrodynamicRelaxation Using Stopless Flow Injection in Split InletSedimentation Field-flow Fractionation’, Anal. Chem.,61, 2439–2444 (1989).

106. M.-K. Liu, P.S. Williams, M.N. Myers, J.C. Giddings,‘Hydrodynamic Relaxation Using Both Split and FritInlets’, Anal. Chem., 63, 2115–2122 (1991).

107. H. Lee, S.K.R. Williams, J.C. Giddings, ‘Particle SizeAnalysis of Dilute Environmental Colloids by FlowField-flow Fractionation Using an Opposed Flow SampleConcentration Technique’, Anal. Chem., 70, 2495–2503(1998).

108. F.J.F. Yang, M.N. Myers, J.C. Giddings, ‘ProgrammedSedimentation Field-flow Fractionation’, Anal. Chem.,46, 1924–1930 (1974).

109. J.C. Giddings, P.S. Williams, R. Beckett, ‘Fractionat-ing Power in Programmed Field-flow Fractionation:Exponential Sedimentation Field Decay’, Anal. Chem.,59, 28–37 (1987).

110. J.C. Giddings, L.K. Smith, M.N. Myers ‘ProgrammedThermal Field-flow Fractionation’, Anal. Chem., 48,1587–1592 (1976).

111. P.S. Williams, J.C. Giddings, R. Beckett, ‘FractionatingPower in Sedimentation Thermal Field-flow Fractiona-tion with Linear and Parabolic Field Decay Program-ming’, J. Liq. Chromatogr., 10, 1961–1998 (1987).

112. W.W. Yau, J.J. Kirkland, ‘Retention Characteristics ofTime-delayed Exponential Field-programmed Sedimen-tation Field-flow Fractionation’, Sep. Sci. Technol., 16,577–605 (1981).

113. J.J. Kirkland, S.W. Rementer, W.W. Yau, ‘Time-delayedExponential Field-programmed Sedimentation Field-flow Fractionation for Particle Distribution Analyses’,Anal. Chem., 53, 1730–1736 (1981).

114. J.J. Kirkland, C.H. Dilks, Jr, ‘Flow Field-flow Fractiona-tion of Polymers in Organic Solvents’, Anal. Chem., 64,2836–2840 (1992).

115. J.J. Kirkland, W.W. Yau, ‘Thermal Field-flow Frac-tionation of Polymers with Exponential TemperatureProgramming’, Macromolecules, 18, 2305–2311 (1985).

116. J.J. Kirkland, S.W. Rementer, W.W. Yau, ‘Molecular-weight Distribution of Polymers by Thermal Field-flowFractionation with Exponential Temperature Program-ming’ Anal. Chem., 60, 610–616 (1988).

117. J.J. Kirkland, W.W. Yau, ‘Thermal Field-flow Fractiona-tion of Water-soluble Macromolecules’, J. Chromatogr.,353, 95–107 (1986).

118. P.S. Williams, J.C. Giddings, ‘Power Programmed Field-flow Fractionation: a New Program Form for ImprovedUniformity of Fractionating Power’, Anal. Chem., 59,2038–2044 (1987).

119. J.C. Giddings, V. Kumar, P.S. Williams, M.N. Myers,‘Polymer Separation by Thermal Field-flow Fraction-ation: High Speed Power Programming’, Adv. Chem.Ser., 227, 3–21 (1990).

120. M.E. Schimpf, J.C. Giddings, ‘Characterization of Ther-mal Diffusion of Copolymers in Solution by ThermalField-flow Fractionation’, J. Polym. Sci., Part B: Polym.Phys., 28, 2673–2680 (1990).

121. A.C. van Asten, E. Venema, W.Th. Kok, H. Poppe, ‘Useof Thermal Field-flow Fractionation for the Fractiona-tion of Polybutadiene in Various Organic Solvents’, J.Chromatogr., 644, 83–94 (1993).

122. A.C. van Asten, R.J. van Dam, W.Th. Kok, R. Tijssen,H. Poppe, ‘Determination of the Compositional Het-erogeneity of Polydisperse Polymer Samples by theCoupling of Size-exclusion Chromatography and Ther-mal Field-flow Fractionation’, J. Chromatogr. A, 703,245–263 (1995).

123. S. Jeon, M.E. Schimpf, ‘Cross-fractionation of Copoly-mers Using SEC and Thermal FFF for Determinationof Molecular Weight and Composition’ in Chromatog-raphy of Polymers: Hyphenated and Multi-dimensionalTechniques, ed. T. Provder, ACS Symposium Series 731,ACS Washington, DC, 141–161, 2000.

124. M.E. Schimpf, J.C. Giddings, ‘Characterization of Ther-mal Diffusion in Polymer Solutions by Thermal Field-flow Fractionation: Dependence on Polymer and SolventParameters’, J. Polym. Sci., Polym. Phys. Ed., 27,1317–1332 (1989).

125. A.C. van Asten, W.Th. Kok, R. Tijssen, H. Poppe,‘Study of the Thermal Diffusion of Polybutadiene andPolytetrahydrofuran in Various Organic Solvents’, J.Polym. Sci., Part B, 34, 297–308 (1996).

126. E. Venema, P. de Leeuw, J.C. Kraak, H. Poppe,R. Tijssen, ‘Polymer Characterization Using On-lineCoupling of Thermal Field-flow Fractionation andHydrodynamic Chromatography’, J. Chromatogr. A,765, 135–144 (1997).

127. S. Lee, A. Molnar, ‘Determination of Molecular Weightand Gel Content of Natural Rubber Using Ther-mal Field-flow Fractionation’, Macromolecules, 28,6354–6356 (1995).

128. P.M. Shiundu, E.E. Remsen, J.C. Giddings, ‘Isolationand Characterization of Polymeric and Particulate Com-ponents of Acrylonitrile–Butadiene–Styrene (ABS)Plastics by Thermal Field-flow Fractionation’, J. Appl.Polym. Sci., 60, 1695–1707 (1996).

129. A. Subramanian, ‘Gel Permeation Chromatography ofNatural Rubber’, Rubber Chem. Technol., 45, 346–358(1972).

130. D. McIntyre, A.L. Shis, J. Saroca, R. Seeger, A. MacAr-thur, ‘Shear Degradation of Very High MolecularWeight Polymers in Gel Permeation Chromatography’,ACS Symp. Ser., 245, 227–240 (1984).

131. S.K. Ratanathanawongs, P.M. Shiundu, J.C. Giddings,‘Size and Compositional Studies of Core-shell Latexes


Using Flow and Thermal Field-flow Fractionation’,Colloids Surf. A: Physicochem. Eng. Aspects, 105,243–250 (1995).

132. P.M. Shiundu, J.C. Giddings, ‘Influence of Bulk and Sur-face Composition on the Retention of Colloidal Particlesin Thermal Field-flow Fractionation’, J. Chromatogr.,715, 117–126 (1995).

133. S.J. Jeon, M.E. Schimpf, A. Nyborg, ‘CompositionalEffects in the Retention of Colloids by ThermalField-flow Fractionation’, Anal. Chem., 69, 3442–3450(1997).

134. J.C. Giddings, M.N. Myers, G.C. Lin, M. Martin, ‘Poly-mer Analysis and Characterization by Field-flow Frac-tionation (One Phase Chromatography)’, J. Chro-matogr., 142, 23–38 (1977).

135. J.C. Giddings, G.C. Lin, M.N. Myers, ‘Fractionation andSize Distribution of Water Soluble Polymers by FlowField-flow Fractionation’, J. Liq. Chromatogr., 1, 1–20(1978).

136. E.A. Bekturov, Z.Kh. Bakauova, Synthetic Water-solublePolymers in Solution, Huthig & Wepf, Basle, 1986.

137. M.-A. Benincasa, ‘Synthetic Polymers – Water Soluble’,in FFF Handbook, eds. M.E. Schimpf, K.D. Caldwell,J.C. Giddings, Wiley Scientific, New York, Chapter III-6, 2000.

138. S. Yanagida, K. Takahashi, M. Okahara, ‘Metal-ionComplexation of Noncyclic Poly(oxyethylene) Deriva-tives. I. Solvent Extraction of Alkali and Alkaline EarthMetal Thiocyanates and Iodides’, Bull. Chem. Soc. Jpn.,50, 1386–1390 (1977).

139. B. Wittgren, K.-G. Wahlund, H. Derand, B. Wesslen,‘Aggregation Behavior of an Amphiphilic Graft Copoly-mer in Aqueous Medium Studied by Asymmetrical FlowField-flow Fractionation’, Macromolecules, 29, 268–276(1996).

140. B. Wittgren, K.-G. Wahlund, H. Derand, B. Wesslen,‘Size Characterization of a Charged AmphiphilicCopolymer in Solution of Different Salts and SaltConcentrations Using Flow Field-flow Fractionation’,Langmuir, 12, 5999–6005 (1996).

141. R. Hanselmann, W. Burchard, M. Ehrat, H.M. Widmer,‘Structural Properties of Fractionated Starch Polymersand Their Dependence on the Dissolution Process’,Macromolecules, 29, 3277–3282 (1996).

142. J.C. Giddings, P.S. Williams, M.-A. Benincasa, ‘RapidBreakthrough Measurement of Void Volume for Field-flow Fractionation Channels’, J. Chromatogr., 627, 23–35(1992).

143. J.M. Davis, ‘Influence of Crossflow Hydrodynamics onRetention Ratio in Flow Field-flow Fractionation’, Anal.Chim. Acta, 246, 161–169 (1991).

144. J.C. Giddings, ‘Micro-FFF: Theoretical and PracticalAspects of Reducing the Dimensions of Field-flow

Fractionation Channels’, J. Microcol. Sep., 5, 497–503(1993).

145. A. Litzen, ‘Separation, Speed, Retention, and Disper-sion in Asymmetrical Flow Field-flow Fractionation asFunctions of Channel Dimensions and Flow Rates’,Anal. Chem., 65, 461–470 (1993).

146. M.N. Myers, W. Cao, C.I. Chien, V. Kumar, J.C. Gidd-ings, ‘Cold Wall Temperature Effects on ThermalField-flow Fractionation’, J. Liq. Chromatogr. Relat.Technol., 20, 2757–2776 (1997).

147. R. Sisson, J.C. Giddings, ‘Effects of Solvent Compositionon Polymer Retention in Thermal Field-flow Frac-tionation: Retention Enhancement in Binary SolventMixtures’, Anal. Chem., 66, 4043–4053 (1994).

148. M.E. Hansen, J.C. Giddings, R. Beckett, ‘Colloid Char-acterization by Sedimentation FFF. VI. Perturbationsdue to Overloading and Electrostatic Repulsion’, J. Col-loid. Interface Sci., 132, 300–312 (1989).

149. J. Janca, M. Martin, ‘Influence of Operational Param-eters on Retention of Ultra-high Molecular WeightPolystyrenes in Thermal Field-flow Fractionation’, Chro-matographia, 34, 125–131 (1992).

150. A.C. van Asten, W.Th. Kok, R. Tijssen, H. Poppe,‘Thermal Field-flow Fractionation of Polytetrahydro-furan’, J. Chromatogr. A, 676, 361–373 (1994).

151. A. Litzen, K.-G. Wahlund, ‘Effects of Temperature,Carrier Composition and Sample Load in AsymmetricalFlow Field-flow Fractionation’, J. Chromatogr., 548,393–406 (1991).

152. A. Carlshaf, J.A. Jonsson, ‘Perturbations of the Reten-tion Parameter Due to Sample Overloading in Hollow-fiber Flow Field-flow Fractionation’, Sep. Sci. Technol.,28, 1191–1201 (1993).

153. J.E.G.J. Wijnhoven, J.-P. Koorn, H. Poppe, W.Th. Kok,‘Influence of Injected Mass and Ionic Strength onRetention of Water-soluble Polymers and Proteins inHollow-fiber Field-flow Fractionation’, J. Chromatogr.A, 732, 307–315 (1996).

154. M. Hoyos, M. Martin, ‘Retention Theory of Sedimenta-tion Field-flow Fractionation at Finite Concentrations’,Anal. Chem., 66, 1718–1730 (1994).

155. J.E.G.J. Wijnhoven, M.R. van Bommel, H. Poppe,W.Th. Kok, ‘Practical Experience with Organic SolventFlow Field-flow Fractionation’, Chromatographia, 42,409–415 (1996).

156. M.-A. Benincasa, unpublished results.157. S.K.R. Williams, J.C. Giddings ‘Sample Recovery’, in

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field flow fractionation in analysis of polymers and rubbers

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